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📝 Translate and solve basic percent equations (15 MCQs)

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

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What is Translate and solve basic percent equations?

Definition:
Translating and solving basic percent equations means converting percent statements like 'What is 30% of 80?' into the equation $P = R \cdot B$ , where $P$ is part, $R$ is rate (decimal), and $B$ is base. Then solve for the unknown using multiplication or division.

Working:
For 'What percent of 40 is 10?' write $10 = R \times 40$ , solve $R = 10/40 = 0.25 = 25\%$ . For '20% of what number is 14?' write $14 = 0.20 \times B$ , so $B = 14/0.20 = 70$ .

Example:
Problem: 'Find 40% of 120.' Equation: $P = 0.40 \times 120 = 48$ .

Reason:
This provides a direct method to handle any percent question, making it a versatile tool for percentage calculations.

Easy

Medium

Hard

📝 All Translate and solve basic percent equations MCQs

Q1. A student translates the statement "18 is what percent of 60?" into $18=0.18(60)$ . Which equation correctly represents the original statement?

18=p(60)

✅

60=p(18)

18=60+p

18=60(100p)

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The unknown is the percentage, so it should be represented by $p$ as a decimal multiplier of the original quantity. Therefore, $18=p(60)$ , and solving gives $p=0.30$ , or 30 percent.

Q2. A store marks an item at Rs. 800 and advertises a discount of 15%. Which equation should be used to find the discount amount $d$ , rather than the final selling price?

d=800-0.15

d=0.15(800)

✅

d=800(1.15)

d=15(800)

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: A percent discount represents a part of the original price, so the discount amount is found by multiplying 800 by 0.15. The equation $d=0.15(800)$ gives Rs. 120, which is the amount reduced.

Q3. A quantity is represented by $x$ . A second quantity is 40% of $x$ , and that second quantity equals 28. Which equation and solution correctly model the situation?

x=0.40(28)

, so

x=11.2

28=0.40x

, so

x=70

✅

28=40x

, so

x=0.7

x=28+0.40

, so

x=28.4

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The phrase "40% of $x$ " translates to $0.40x$ , and that quantity equals 28. Solving $28=0.40x$ requires division by 0.40, producing $x=70$ . The other choices reverse or mishandle the percentage relationship.

Q4. A school reports that 72 students represent 60% of all students in a program. Which reasoning best determines the total enrollment?

A.Multiply 72 by 0.60 to obtain 43.2

B.Divide 72 by 0.60 to obtain 120 ✅

C.Subtract 0.60 from 72 to obtain 71.4

D.Divide 60 by 72 to obtain 83.3

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Because 72 is the known part and 60% is the fraction of the total represented by that part, the equation is $72=0.60x$ . Dividing both sides by 0.60 gives $x=120$ , the total enrollment.

Q5. A worker receives a 12% increase on a monthly salary of Rs. 45,000. If $n$ represents the new salary, which equation correctly models the situation and gives the new salary?

n=45,000+0.12=45,000.12

n=45,000(0.12)=5,400

n=45,000(1.12)=50,400

✅

n=45,000(0.88)=39,600

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: A 12% increase means the new amount contains the original 100% plus another 12%, totaling 112%, or 1.12 times the original. Thus $n=45,000(1.12)=50,400$ , not merely the increase amount.

Q6. A tank contains 36 liters, which is 45% of its full capacity. A student writes $x=36(0.45)$ to find the capacity. What is the correct interpretation?

A.The student is correct because the known amount should be multiplied by the percent

B.The student should subtract 45% from 36

C.The student should solve

36=0.45x

, giving

x=80

liters ✅

D.The student should solve

45=36x

, giving

x=1.25

liters

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The 36 liters represents only 45% of the unknown full capacity. Therefore, the correct model is $36=0.45x$ . Dividing by 0.45 gives 80 liters, showing why multiplying 36 by 0.45 incorrectly makes the quantity smaller.

Q7. A farmer finds that 24% of a field, or 18 acres, is planted with wheat. He wants to determine the entire field area. Which sequence is mathematically justified?

A.Write

18=0.24x

, then divide by 0.24 ✅

B.Write

24=18x

, then divide by 18

C.Write

x=18-0.24

, then subtract again

D.Write

18=x+0.24x

, then add 18

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The phrase "24% of the field is 18 acres" means $0.24x=18$ . Solving this equation by dividing both sides by 0.24 gives $x=75$ acres. This preserves the part-to-whole relationship.

Q8. A learner solves $0.35x=42$ as follows: “Since 35% is 0.35, I multiply 42 by 0.35 and get 14.7.” What is the specific error?

A.The learner converted 35% into 35 instead of 0.35

B.The learner multiplied by the percentage when the equation requires division by the coefficient ✅

C.The learner should have added 35 to 42

D.The learner should have divided 42 by 35 and then multiplied by 100

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: In $0.35x=42$ , 42 is the result of taking 35% of $x$ . To recover the original whole, the operation must be reversed by dividing 42 by 0.35. This gives $x=120$ , not 14.7.

Q9. A retailer says, “After a 20% discount, the price is Rs. 960.” A student models this as $960=0.20x$ . Another student models it as $960=0.80x$ . Which student is correct, and why?

A.The first student, because 20% is the selling price

B.The first student, because discounts are always multiplied by the final price

C.The second student, because 80% of the original price remains after a 20% discount ✅

D.Both students, because 20% and 80% produce the same result

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: A 20% discount removes 20% of the original price, leaving 80%. Therefore, the final price satisfies $960=0.80x$ . Solving gives $x=1,200$ , whereas $0.20x=960$ would incorrectly treat the discount itself as the final price.

Q10. A graph represents the equation $y=0.25x$ . Which point on the graph would allow a student to conclude that 25% of 80 equals 20?

(20, 80)

(80, 20)

✅

(25, 80)

(80, 25)

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: For $y=0.25x$ , the output $y$ is 25% of the input $x$ . Substituting $x=80$ gives $y=20$ , so the graph must contain the point $(80,20)$ . The coordinate order is essential.

Q11. A graph of $y=px$ passes through the point $(50,15)$ . If $p$ represents a percentage written as a decimal, which statement is supported by the graph?

A.15 is 50% of the unknown quantity

B.50 is 15% of the unknown quantity

C.15 is 30% of 50 ✅

D.50 is 30% of 15

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The slope $p$ is found from $15/50=0.30$ . Thus the graph represents $y=0.30x$ , meaning 15 is 30% of 50. This interpretation connects the graph's slope directly to the percent multiplier.

Q12. A company estimates that 8% of its 1,250 customers will respond to an offer. The response count is represented by $r$ . Which model and conclusion are most reasonable?

r=8(1,250)

, so

r=10,000

r=0.08(1,250)

, so

r=100

✅

r=1,250/0.08

, so

r=15,625

r=1,250-0.08

, so

r=1,249.92

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The response rate of 8% means 0.08 of the customer population is expected to respond. Therefore, $r=0.08(1,250)=100$ . The result is also reasonable because a small percentage of 1,250 should produce a much smaller count.

Q13. A student must find a number whose 125% equals 250. Student A writes $250=1.25x$ . Student B writes $x=250(1.25)$ . Which approach correctly finds the original number?

A.Student A, because

x=200

after dividing by 1.25 ✅

B.Student B, because multiplying by 1.25 reverses the percentage

C.Both, because both produce

x=312.5

D.Neither, because 125% cannot be represented as a decimal

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Since 125% equals 1.25, the statement translates to $250=1.25x$ . Dividing by 1.25 recovers the original number, $x=200$ . Multiplication would increase 250 and therefore cannot recover a smaller original quantity.

Q14. A price is increased by 25% and then reduced by 25%. A student claims the final price must equal the original because the same percentage was added and removed. If the original price is Rs. 400, what is the correct final price?

A.Rs. 350

B.Rs. 375 ✅

C.Rs. 400

D.Rs. 425

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The increase gives $400(1.25)=500$ . The 25% reduction is calculated from the new price, so the final amount is $500(0.75)=375$ . Equal percentages do not cancel because they are applied to different base amounts.

Q15. A number is increased by 20%, then the result is increased by another 20%. The final value is 432. Which equation correctly represents the original number $x$ , and what is $x$ ?

432=1.20x

, so

x=360

432=1.40x

, so

x\approx308.57

432=(1.20)(1.20)x

, so

x=300

✅

432=(0.20)(0.20)x

, so

x=10,800

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Each 20% increase multiplies the current amount by 1.20, so two successive increases produce $432=(1.20)(1.20)x=1.44x$ . Dividing 432 by 1.44 gives $x=300$ . The percentages compound rather than simply adding.

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