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📝 How to calculate sale price after discount (15 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 15 questions available

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What is How to calculate sale price after discount?

Definition:
The sale price is the final price a customer pays after a discount is applied to the original price, calculated by subtracting the discount amount from the original price, or by multiplying the original price by the complement of the discount rate (i.e., $1 - \text{discount rate}$ ), giving the formula $\text{Sale Price} = \text{Original Price} - (\text{Original Price} \times \text{Discount Rate})$ or $\text{Sale Price} = \text{Original Price} \times (1 - \text{Discount Rate})$ .

Working:
To calculate the sale price, first convert the discount percentage to a decimal, then either subtract the product of the original price and the discount rate from the original price, or directly multiply the original price by the remaining percentage expressed as a decimal (e.g., for a 20% discount, multiply by 0.80), and the result is the amount the customer pays.

Example:
If a $\120 \) pair of shoes is discounted by 30%, the sale price is $120 \times (1 - 0.30) = 120 \times 0.70 = \84$ , or alternatively, $120 - (120 \times 0.30) = 120 - 36 = \84 \), so the customer pays $\84$ .

Reason:
Calculating the sale price is critical for consumers to budget their purchases, for retailers to determine final pricing strategies, and for analyzing the effectiveness of discount promotions, ensuring both buyers and sellers understand the final transaction amount.

Easy

Medium

Hard

📝 All How to calculate sale price after discount MCQs

Q1. A jacket has a marked price of $\$80$ and is discounted by $25\%$ . What is its sale price?

\$55

\$60

✅

\$65

\$70

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The discount is $25\%$ of $\80$ , which is $0.25(80)=\20$ . Subtracting the discount from the original price gives $80-20=\60 \). The sale price is therefore $\60$ .

Q2. A store advertises a $30\%$ discount on a backpack priced at $\$50$ . Which expression correctly represents the sale price?

50(0.30)

50-0.30

50(1-0.30)

✅

50(1+0.30)

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: A discount removes $30\%$ of the original price, so $70\%$ remains. The sale price is therefore represented by $50(1-0.30)=50(0.70)$ . The other expressions either calculate only the discount or change the price incorrectly.

Q3. Two stores sell the same tablet for $\240 \). Store A offers $20\%$ off, while Store B reduces the price by $\48$ . Which statement is correct?

A.Store A is cheaper by

\$48

B.Store B is cheaper by

\$48

C.Both stores have the same sale price ✅

D.Store A is cheaper by

\$24

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: A $20\%$ discount on $\240$ is $0.20(240)=\48$ . Store A therefore charges $240-48=\192 \). Store B also charges $240-48=\192$ , so the two sale prices are identical.

Q4. A customer claims that a $15\%$ discount on a $\120 \) item means the customer pays $\105$ . Which evaluation best identifies the error?

A.The discount should be added, giving

\$138

B.The discount is

\<span class="katex-error" title="ParseError: KaTeX parse error: Can&#x27;t use function &#x27;

' in math mode at position 4: 18 \̲)̲, so the sale p…" style="color:#cc0000">18 \), so the sale price is

\</span>102

✅

C.The discount is

\<span class="katex-error" title="ParseError: KaTeX parse error: Can&#x27;t use function &#x27;

' in math mode at position 4: 15 \̲)̲, so the sale p…" style="color:#cc0000">15 \), so the sale price is

\</span>105

D.The sale price should remain

\$120

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The discount is calculated from the original price: $0.15(120)=\18 \). Therefore, the customer pays $120-18=\102$ . The mistake is treating $15\%$ as a fixed $\15 \) reduction instead of calculating $15\%$ of $\120$ .

Q5. A store marks a bicycle at $\360 \), then applies a $25\%$ discount. A customer has $\300$ . After the discount, how much money remains?

\$30

✅

\$40

\$50

\$60

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The discount equals $0.25(360)=\90 \). The sale price is $360-90=\270$ . Since the customer has $\300 \), the remaining amount is $300-270=\30$ . Thus the correct answer is actually $\$30$ .

Q6. A furniture store offers $35\%$ off a sofa priced at $\800 \). The customer also receives a fixed $\40$ coupon after the percentage discount. What is the final amount paid?

\$480

✅

\$500

\$520

\$540

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The $35\%$ discount is $0.35(800)=\280$ , leaving $800-280=\520$ . Applying the additional $\40 \) coupon gives $520-40=\480$ . The key is applying the percentage discount before the fixed coupon.

Q7. A graph represents sale price $S$ versus original price $P$ for a store offering a constant $20\%$ discount. Which relationship should the graph display?

S=0.20P

S=0.80P

✅

S=P+0.20

S=1.20P

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: A $20\%$ discount means the customer keeps $100\%-20\%=80\%$ of the original price. Therefore the sale price is $S=0.80P$ . A graph of this relationship should be a straight line through the origin with slope $0.80$ .

Q8. A graph shows the following price pairs: $(100,85)$ , $(200,170)$ , and $(400,340)$ , where each pair is $(\text{original price},\text{sale price})$ . What discount rate does the graph represent?

10\%

15\%

✅

20\%

25\%

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Each sale price is $85\%$ of the original price: $85/100=0.85$ , $170/200=0.85$ , and $340/400=0.85$ . Therefore, $15\%$ has been removed from every original price, indicating a $15\%$ discount.

Q9. A customer compares two offers for a $\$500$ appliance. Offer A gives $30\%$ off. Offer B gives $20\%$ off followed by another $10\%$ off the reduced price. Which offer has the lower sale price?

A.Offer A, by

\$5

✅

B.Offer B, by

\$5

C.Both have the same sale price

D.Offer B, by

\$10

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: Offer A gives $500(0.70)=\350 \). Offer B gives $500(0.80)=\400$ , followed by $400(0.90)=\360 \). Therefore, Offer A is cheaper by $\10$ , not $\$5$ .

Q10. A student calculates the sale price of a $\250$ item with a $12\%$ discount as $250(1.12)=\280$ . What mistake did the student make?

A.They calculated

12\%

of the price correctly but subtracted twice

B.They increased the original price instead of reducing it ✅

C.They used the wrong original price

D.They converted

12\%

into

0.012

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Multiplying by $1.12$ increases the price by $12\%$ , which represents a markup rather than a discount. For a $12\%$ discount, the remaining fraction is $1-0.12=0.88$ , giving a sale price of $250(0.88)=\$220$ .

Q11. A store's sales data shows original prices of $\50,\100,\150,\200$ and corresponding sale prices of $\45,\90,\135,\180$ . If the same pattern continues, what is the sale price of an item originally priced at $\$320$ ?

\$272

\$280

\$288

✅

\$300

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The data show that every sale price is $90\%$ of the original price. Thus the discount rate is $10\%$ . For $\320 \), the sale price is $320(0.90)=\288$ , following the same linear pattern shown by the data.

Q12. A clothing store offers $40\%$ off a $\75 \) shirt. A second store sells the same shirt for $\44$ after a $\6 \) coupon is applied to its already discounted price. If the second store's original price was $\80$ with a $35\%$ discount, which store is cheaper?

A.First store by

\$5

B.Second store by

\$5

C.First store by

\$1

✅

D.Both stores have the same price

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The first store's price is $75(0.60)=\45 \). The second store's percentage discount gives $80(0.65)=\52$ , and the $\6 \) coupon reduces it to $\46$ . Therefore, the first store is actually cheaper by $\$1$ , so none of the listed choices is correct.

Q13. An item is discounted by $18\%$ , and its sale price is $\$246$ . What was the original price?

\$280

\$290

\$300

✅

\$320

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: After an $18\%$ discount, $82\%$ of the original price remains. Let the original price be $P$ . Then $0.82P=246$ , so $P=246/0.82=\$300$ . This requires working backward rather than simply subtracting $18\%$ from the sale price.

Q14. A merchant offers a $25\%$ discount on an item. A customer argues that if the merchant later gives an additional $25\%$ discount, the item becomes free because $25\%+25\%=50\%$ . Which reasoning is correct?

A.The item becomes

50\%

cheaper

B.The second discount is calculated from the original price

C.The second discount is calculated from the already reduced price ✅

D.The two discounts cancel each other

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Percentage discounts applied successively are based on the current price, not always the original price. After the first $25\%$ discount, $75\%$ remains. A second $25\%$ discount leaves $75\%(75\%)=56.25\%$ , so the total reduction is $43.75\%$ , not $50\%$ .

Q15. A rare item has a marked price of $\$1,200$ . Store X offers $45\%$ off. Store Y first reduces the price by $30\%$ and then gives an additional $20\%$ off the reduced price. Which store gives the lower sale price, and by how much?

A.Store X by

\$24

✅

B.Store Y by

\$24

C.Store X by

\$36

D.Store Y by

\$36

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: Store X charges $1200(0.55)=\660 \). Store Y charges $1200(0.70)(0.80)=\672$ . Therefore, Store X gives the lower price, and the difference is $672-660=\$12$ , so the listed options are inconsistent with the calculation.

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