MathBored

Virginia SOL Mathematics Textbook

Grade 8 Workbook — Chapter 3: Percent Applications: Discounts, Markups, Tax, and Tip

SOL 8.CE.1 · Companion to Textbook Chapter 3

Each page below is one Canva page. Headings are sized for direct paste: page title as H1, section labels as H2. Figures referenced by filename live in ../figures/. Every numbered item is the same problem as in the textbook, so one answer key serves both. Item numbers run continuously from 1 to 132.

PAGE 1 — Chapter opener

Chapter 3 · Percent Applications

Standard 8.CE.1

In this chapter you will:

Words to know: percent · benchmark percentage · estimate · discount · discount amount · sale price · complement multiplier · cost · markup · markup amount · selling price · sales tax · subtotal · total · tip · original amount · new amount · amount of change · percent increase · percent decrease

Money rule: round every dollar amount to the nearest cent, rounding a half cent up. Round once, at the end.

One-discount rule: every problem in this chapter applies exactly one discount or one markup. Never two.

PAGE 2 — A percent of a price

3.1 Estimating and Finding a Percent of a Price

FIGURE: fig1-percent-of-a-price.png (full width)

Fill in the blanks.

To find 10%10\% of a price, move the decimal point ________ place(s) to the ________.

To find 1%1\% of a price, move the decimal point ________ place(s) to the ________.

To find 5%5\%, first find ________, then ________ it.

15%=15\% = ________ ++ ________

The decimal point that moves belongs to the ____________, not to the percent.

Guided practice.

  1. 10%10\% of $46.00=\$46.00 = ______

  2. 5%5\% of $46.00=\$46.00 = ______

  3. 1%1\% of $84.00=\$84.00 = ______

  4. 25%25\% of $36.80=\$36.80 = ______

PAGE 3 — Estimate, then compute

Estimating with Benchmarks

FIGURE: fig7-estimate-then-check.png (full width)

  1. Estimate 20%20\% of $38.75\$38.75 by rounding the price to $40.00\$40.00.

    Estimate: $______

  2. 15%15\% of $52.00=\$52.00 = ______

    Show your benchmark work: 10%10\% is ______ and 5%5\% is ______

Independent practice.

  1. Find each amount.
a) 20%20\% of $65.00\$65.00 b) 30%30\% of $24.50\$24.50 c) 6%6\% of $120.00\$120.00 d) 2.5%2.5\% of $80.00\$80.00

  1. 5.3%5.3\% of $40.00=\$40.00 = ______

  2. 18%18\% of $63.50=\$63.50 = ______

PAGE 4 — Rounding and reasoning

Rounding Money to the Nearest Cent

  1. Round each to the nearest cent.
a) $7.3125\$7.3125 b) $12.995\$12.995 c) $0.4449\$0.4449

  1. Estimate 15%15\% of $79.40\$79.40, then compute it exactly.

    Estimate: $______ Exact: $______ Off by: $______

  2. Explain. Why can 1%1\% of a price be found by moving the decimal point two places left?

  3. Apply it. A jacket is priced at $74.00\$74.00. Find 30%30\% of that price. $______

  4. Find the error. To find 8%8\% of $45.00\$45.00, a student computes 8×45=3608 \times 45 = 360 and writes $360.00.

    What went wrong? _______________________________________________

    Correct amount: $______

PAGE 5 — Exit ticket 3.1

Exit Ticket 3.1

  1. 10%10\% of $27.40=\$27.40 = ______

  2. 5%5\% of $62.00=\$62.00 = ______

  3. 12%12\% of $95.00=\$95.00 = ______

  4. Estimate 20%20\% of $41.20\$41.20.

    Estimate: $______

    Is your estimate high or low? ____________ Why?

PAGE 6 — Discounts

3.2 Discounts and Sale Prices

FIGURE: fig2-discount-two-routes.png (full width)

Fill in the blanks.

discount amount == ____________ ×\times ____________

sale price == ____________ −- ____________

For a 20%20\% discount, the complement multiplier is ________.

For a discount rate rr, sale price =(= ( ________ )×) \times original price.

Guided practice.

  1. A $60.00\$60.00 backpack is 20%20\% off. Discount amount: $______

  2. Sale price of that backpack: $______

  3. A $45.00\$45.00 pair of shoes is 10%10\% off. Sale price: $______

  4. A $32.00\$32.00 game is 25%25\% off. Use the complement multiplier. Sale price: $______

PAGE 7 — Discount practice

Finding Discounts and Sale Prices

  1. A $120.00\$120.00 bike is 15%15\% off.

    Discount: $______ Sale price: $______

  2. Estimate the sale price of a $39.80\$39.80 lamp at 25%25\% off, rounding the price to $40.00\$40.00.

    Estimate: $______

  3. Find the discount amount and the sale price.

Item Discount amount Sale price
a) $80.00\$80.00 at 35%35\% off
b) $24.50\$24.50 at 20%20\% off
c) $18.60\$18.60 at 50%50\% off
d) $149.99\$149.99 at 40%40\% off
  1. A $72.00\$72.00 coat is 30%30\% off. Sale price: $______

PAGE 8 — Discount application and reasoning

Discounts in Context

  1. A $56.40\$56.40 tent is 15%15\% off.

    Discount: $______ Sale price: $______

  2. A $99.00\$99.00 chair is 45%45\% off. Sale price: $______

  3. Explain. Why does multiplying the original price by 0.800.80 give the sale price when an item is 20%20\% off?

  4. Apply it. A store advertises 60%60\% off a $85.00\$85.00 coat.

    Amount saved: $______ Cost of the coat: $______

  5. Find the error. Asked for the sale price of a $48.00\$48.00 item at 30%30\% off, a student answers $14.40.

    What did the student find? ____________________ Sale price: $______

  6. Estimate, then check. A $61.75\$61.75 sweater is 20%20\% off.

    Estimate: $______ Exact sale price: $______ High or low? ________

PAGE 9 — Exit ticket 3.2

Exit Ticket 3.2

  1. A $40.00\$40.00 item is 25%25\% off. Sale price: $______

  2. A $65.00\$65.00 item is 10%10\% off. Discount amount: $______

  3. A $36.80\$36.80 item is 50%50\% off. Sale price: $______

  4. Explain. Why do subtracting the discount and multiplying by the complement give the same sale price?

PAGE 10 — Markups

3.3 Markups and Selling Prices

FIGURE: fig3-markup-bar.png (full width)

Fill in the blanks.

markup amount == ____________ ×\times ____________

selling price == ____________ ++ ____________

For a 25%25\% markup, the multiplier is ________.

A discount multiplier is always ________ than 1. A markup multiplier is always ________ than 1.

Guided practice.

  1. An item costs $40.00\$40.00 and is marked up 25%25\%. Markup amount: $______

  2. Selling price of that item: $______

  3. Cost $18.00\$18.00, markup 50%50\%. Selling price: $______

  4. Cost $62.00\$62.00, markup 10%10\%. Selling price: $______

PAGE 11 — Markup practice

Finding Markups and Selling Prices

  1. Cost $85.00\$85.00, markup 40%40\%.

    Markup: $______ Selling price: $______

  2. Estimate the selling price of an item costing $29.60\$29.60 with a 30%30\% markup, rounding the cost to $30.00\$30.00.

    Estimate: $______

  3. Find the markup amount and the selling price.

Item Markup amount Selling price
a) cost $24.00\$24.00, markup 15%15\%
b) cost $150.00\$150.00, markup 20%20\%
c) cost $9.50\$9.50, markup 60%60\%
d) cost $47.25\$47.25, markup 40%40\%
  1. Cost $36.80\$36.80, markup 35%35\%. Selling price: $______

PAGE 12 — Markup application and reasoning

Markups in Context

  1. Cost $112.00\$112.00, markup 45%45\%.

    Markup: $______ Selling price: $______

  2. A shop marks up a $14.60\$14.60 item by 55%55\%. Selling price: $______

  3. Explain. Why is the multiplier for a 25%25\% markup equal to 1.251.25, and why is a markup multiplier always greater than 1?

  4. Apply it. A bakery spends $8.40\$8.40 on ingredients for one cake and marks it up 125%125\%.

    Markup: $______ Selling price: $______

  5. Find the error. Asked for the selling price of a $50.00\$50.00 item with a 30%30\% markup, a student answers $15.00.

    What did the student find? ____________________ Selling price: $______

  6. Estimate, then check. Cost $78.40\$78.40, markup 25%25\%.

    Estimate: $______ Exact selling price: $______

PAGE 13 — Exit ticket 3.3

Exit Ticket 3.3

  1. Cost $20.00\$20.00, markup 30%30\%. Selling price: $______

  2. Cost $64.00\$64.00, markup 25%25\%. Markup amount: $______

  3. Cost $45.50\$45.50, markup 20%20\%. Selling price: $______

  4. Explain. What is the difference between a discount and a markup, and what does each do to the multiplier?

PAGE 14 — Sales tax

3.4 Sales Tax and the Total

FIGURE: fig4-tax-total-bar.png (full width)

Fill in the blanks.

tax == ____________ ×\times ____________

total == ____________ ++ ____________

At a 5.3%5.3\% rate, the total is ________ %\% of the price, so the one-step multiplier is ________.

A tax problem asks for the ____________, not just the tax.

Guided practice.

  1. 5.3%5.3\% of $40.00=\$40.00 = ______

  2. Purchase $40.00\$40.00, tax rate 5.3%5.3\%. Total: $______

  3. Purchase $25.00\$25.00, tax rate 6%6\%.

    Tax: $______ Total: $______

  4. Purchase $18.00\$18.00, tax rate 5.3%5.3\%. Total: $______

PAGE 15 — Tax practice

Finding Tax and Totals

  1. Grocery order $63.00\$63.00, reduced rate 1%1\%. Total: $______

  2. Estimate the total on a $59.80\$59.80 purchase at 5.3%5.3\%, rounding the price to $60.00\$60.00 and the rate to 5%5\%.

    Estimate: $______

  3. Find the tax and the total.

Purchase Tax Total
a) $32.00\$32.00 at 5.3%5.3\%
b) $75.00\$75.00 at 6%6\%
c) $120.50\$120.50 at 5.3%5.3\%
d) $14.99\$14.99 at 7%7\%
  1. Purchase $248.00\$248.00, tax rate 5.3%5.3\%. Total: $______

PAGE 16 — Tax application and reasoning

Tax in Context

  1. Purchase $8.75\$8.75, tax rate 6%6\%.

    Tax: $______ Total: $______

  2. Purchase $52.40\$52.40, tax rate 5.3%5.3\%. Total: $______

  3. Explain. Why is the total on a purchase taxed at 5.3%5.3\% equal to 105.3%105.3\% of the price?

  4. Apply it. Two concert tickets cost $21.50\$21.50 each. The tax rate is 6%6\%.

    Subtotal: $______ Tax: $______ Total: $______

  5. Find the error. Asked for the total cost of a $40.00\$40.00 purchase at 5.3%5.3\% tax, a student answers $2.12.

    What did the student find? ____________________ Total: $______

  6. Estimate, then check. Purchase $79.60\$79.60 at 5.3%5.3\%.

    Estimate: $______ Exact total: $______

PAGE 17 — Exit ticket 3.4

Exit Ticket 3.4

  1. Purchase $30.00\$30.00, tax rate 5.3%5.3\%.

    Tax: $______ Total: $______

  2. Purchase $45.00\$45.00, tax rate 6%6\%. Total: $______

  3. Purchase $12.80\$12.80, tax rate 5.3%5.3\%. Total: $______

  4. Explain. Why is estimating Virginia's 5.3%5.3\% tax with 5%5\% close, and does the estimated tax come out high or low?

PAGE 18 — Tips

3.5 Tip and the Total

FIGURE: fig5-tip-benchmarks.png (full width)

Fill in the blanks.

tip == ____________ ×\times ____________

total == ____________ ++ ____________

For a 20%20\% tip, the one-step multiplier is ________.

In this book, the tip is computed on the ____________ bill.

Guided practice.

  1. Bill $40.00\$40.00, tip 15%15\%.

    Tip: $______ Total: $______

  2. Bill $35.00\$35.00, tip 20%20\%.

    Tip: $______ Total: $______

  3. Bill $50.00\$50.00, tip 18%18\%.

    Tip: $______ Total: $______

PAGE 19 — Tip practice

Finding Tips and Totals

  1. Bill $62.00\$62.00, tip 15%15\%.

    Tip: $______ Total: $______

  2. Bill $24.60\$24.60, tip 20%20\%.

    Tip: $______ Total: $______

  3. Estimate a 15%15\% tip on a $38.40\$38.40 bill by rounding the bill to $40.00\$40.00. Estimate: $______

  4. Find the tip and the total.

Bill and tip rate Tip Total
a) $56.00\$56.00 bill, 15%15\%
b) $83.00\$83.00 bill, 20%20\%
c) $27.50\$27.50 bill, 18%18\%
d) $46.75\$46.75 bill, 15%15\%
  1. Bill $72.80\$72.80, tip 20%20\%. Total: $______

PAGE 20 — Tip application and reasoning

Tips in Context

  1. Bill $19.99\$19.99, tip 18%18\%.

    Tip: $______ Total: $______

  2. Group bill $118.00\$118.00, tip 18%18\%. Total: $______

  3. Explain. Describe the "find 10%10\%, then add half of it" method for a 15%15\% tip, and say why it works.

  4. Apply it. A meal costs $64.00\$64.00. Tax is 6%6\% and the tip is 20%20\% of the pre-tax bill.

    Tax: $______ Tip: $______ Total: $______

  5. Find the error. A diner computes a 20%20\% tip on a $45.00\$45.00 bill as $9.00 and leaves $9.00 on the table as payment for the whole meal.

    What went wrong? _______________________________________________

    Amount that should be paid: $______

  6. Estimate, then check. Bill $47.30\$47.30, tip 20%20\%.

    Estimate of the total: $______ Exact total: $______ Off by: $______

PAGE 21 — Exit ticket 3.5

Exit Ticket 3.5

  1. Bill $20.00\$20.00, tip 15%15\%.

    Tip: $______ Total: $______

  2. Bill $41.50\$41.50, tip 20%20\%.

    Tip: $______ Total: $______

  3. Bill $36.00\$36.00, tip 18%18\%.

    Tip: $______ Total: $______

  4. Explain. Why is a bill-plus-tip total always more than 100%100\% of the bill?

PAGE 22 — Percent increase and decrease

3.6 Percent Increase and Percent Decrease

FIGURE: fig6-percent-change.png (full width)

Fill in the blanks.

percent change=‾‾×100%\text{percent change} = \frac{\underline{\hspace{3cm}}}{\underline{\hspace{3cm}}} \times 100\%

The denominator is always the ____________ amount, never the ____________ amount.

If the amount went up it is a percent ____________. If it went down it is a percent ____________.

Guided practice.

  1. A price rises from $40.00\$40.00 to $46.00\$46.00.

    Amount of increase: $______ Percent increase: ______ %\%

  2. A price falls from $50.00\$50.00 to $42.00\$42.00.

    Amount of decrease: $______ Percent decrease: ______ %\%

  3. $25.00\$25.00 to $30.00\$30.00. Percent increase: ______ %\%

  4. $80.00\$80.00 to $60.00\$60.00. Percent decrease: ______ %\%

PAGE 23 — Percent change practice

Finding a Percent Change

  1. $12.00\$12.00 to $13.50\$13.50. Percent increase: ______ %\%

  2. $36.00\$36.00 to $27.00\$27.00. Increase or decrease? ____________ Percent: ______ %\%

  3. Find the percent change and name it an increase or a decrease.

Change Amount of change Percent Increase or decrease
a) $20.00\$20.00 to $26.00\$26.00
b) $75.00\$75.00 to $60.00\$60.00
c) $48.00\$48.00 to $54.00\$54.00
d) $9.60\$9.60 to $8.40\$8.40

  1. Rent rises from $850.00\$850.00 to $901.00\$901.00. Percent increase: ______ %\%

  2. Attendance falls from 240 people to 216 people. Percent decrease: ______ %\%

PAGE 24 — Percent change application and reasoning

Percent Change in Context

  1. A phone plan goes from $45.00\$45.00 to $49.50\$49.50. Percent increase: ______ %\%

  2. A bike listed at $180.00\$180.00 sells for $153.00\$153.00. Percent decrease: ______ %\%

  3. Explain. Why is the original amount always the denominator? Use $40.00\$40.00 rising to $50.00\$50.00 and show what you get if you divide by the new amount instead.

    Dividing by the original: ______ %\% Dividing by the new: ______ %\%

  4. Apply it. A town's recycling rises from 1,250 tons to 1,400 tons. Percent increase: ______ %\%

  5. Find the error. A student says $60.00\$60.00 rising to $75.00\$75.00 is a 20%20\% increase because 1575=0.20\frac{15}{75} = 0.20.

    What went wrong? _______________________________________________

    Correct percent increase: ______ %\%

PAGE 25 — Exit ticket 3.6

Exit Ticket 3.6

  1. $50.00\$50.00 to $58.00\$58.00. Percent increase: ______ %\%

  2. $120.00\$120.00 to $96.00\$96.00. Percent decrease: ______ %\%

  3. $16.00\$16.00 to $18.40\$18.40. Percent increase: ______ %\%

  4. Explain. What is the difference between "the price decreased by 20%20\%" and "the new price is 20%20\% of the original price"?

PAGE 26 — Chapter 3 review, part 1

Chapter 3 Review

Part A · One discount or one markup

  1. A $95.00\$95.00 item is 20%20\% off.

    Discount: $______ Sale price: $______

  2. A $42.60\$42.60 item is 25%25\% off. Sale price: $______

  3. Cost $56.00\$56.00, markup 30%30\%. Selling price: $______

  4. Cost $23.40\$23.40, markup 45%45\%. Selling price: $______

  5. Estimate, then compute. A $118.50\$118.50 item is 40%40\% off.

    Estimate: $______ Exact sale price: $______

  6. Apply it. A coat priced at $68.00\$68.00 is 15%15\% off.

    Amount saved: $______ Cost of the coat: $______

PAGE 27 — Chapter 3 review, part 2

Chapter 3 Review (continued)

Part B · Sales tax, tip, and the total

  1. Purchase $64.00\$64.00 at 5.3%5.3\% tax. Total: $______

  2. Purchase $31.25\$31.25 at 6%6\% tax.

    Tax: $______ Total: $______

  3. Bill $54.00\$54.00, tip 18%18\%. Total: $______

  4. Bill $88.40\$88.40, tip 20%20\%. Total: $______

  5. Grocery order $27.90\$27.90 at the 1%1\% rate. Total: $______

  6. Apply it. A meal costs $45.60\$45.60. Tax is 6%6\% and the tip is 15%15\% of the pre-tax bill.

    Tax: $______ Tip: $______ Total: $______

PAGE 28 — Chapter 3 review, part 3

Chapter 3 Review (continued)

Part C · Percent increase and percent decrease

  1. $80.00\$80.00 to $92.00\$92.00. Percent increase: ______ %\%

  2. $150.00\$150.00 to $120.00\$120.00. Percent decrease: ______ %\%

  3. $18.00\$18.00 to $20.70\$20.70. Percent increase: ______ %\%

  4. Membership falls from 320 to 272. Percent decrease: ______ %\%

  5. $64.00\$64.00 to $72.00\$72.00. Percent increase: ______ %\%

  6. A jacket falls from $96.00\$96.00 to $81.60\$81.60. Percent decrease: ______ %\%

PAGE 29 — Chapter 3 review, part 4

Chapter 3 Review (continued)

Part D · Application and reasoning

  1. Apply it. A $54.00\$54.00 pair of jeans is 25%25\% off, and 5.3%5.3\% sales tax is charged on the sale price.

    Sale price: $______ Tax: $______ Total: $______

  2. Apply it. A restaurant bill is $78.50\$78.50 with a 20%20\% tip.

    Tip: $______ Total: $______

  3. Explain. Why is the multiplier for a 35%35\% discount 0.650.65 while the multiplier for a 35%35\% markup is 1.351.35?

  4. Find the error. A student finds the percent decrease from $80.00\$80.00 to $68.00\$68.00 as about 17.6%17.6\%, using 1268\frac{12}{68}.

    What went wrong? _______________________________________________

    Correct percent decrease: ______ %\%

  5. Estimate and judge. Without computing exactly, does a $29.90\$29.90 item at 30%30\% off cost more or less than $20.00\$20.00?

    Circle one: MORE LESS

    Justify: _______________________________________________

    Exact sale price: $______

  6. Explain. One store raises a price from $40.00\$40.00 to $50.00\$50.00. Another lowers a price from $50.00\$50.00 to $40.00\$40.00. Both moved by $10.00\$10.00.

    Percent increase: ______ %\% Percent decrease: ______ %\%

    Are they equal? ________ Why or why not?

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