← Back to 3. Mathematical Models in Algebra

📝 Finding the Whole Given a Part and Percent (12 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 12 questions available

←Previous Topic:Finding what percent one number is of another📝 Finding the Whole Given a Part and PercentFind percent increase:Next Topic→

What is Finding the Whole Given a Part and Percent?

Definition:
Finding the whole given a part and percent means determining the total amount when you know a portion and its corresponding percentage. Use the formula $\text{Whole} = \text{Part} / \text{Percent (as decimal)}$ . For example, if 24 is 40% of a number, find the number: $24 / 0.40 = 60$ .

Working:
Step 1: Convert the percent to a decimal. Step 2: Divide the part by this decimal. For example, '15 is 25% of what number?' $15 / 0.25 = 60$ .

Example:
Problem: '18 is 30% of what number?' $18 / 0.30 = 60$ . The whole is 60.

Reason:
This is essential for finding original values from discounts, tax calculations, or determining total populations from sample data.

Easy

Medium

Hard

📝 All Finding the Whole Given a Part and Percent MCQs

Q1. A student correctly identifies that 18 is 30% of a number. Which equation best represents the situation and why?

0.30x=18

, because 18 is the percentage part of the whole

x

✅

18x=0.30

, because the part is multiplied by the whole

30x=18

, because percentages should be written as whole numbers

0.30+18=x

, because the whole combines the percent and part

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The percentage relationship is part = percent × whole. Since 30% is $0.30$ and the known part is 18, the correct model is $0.30x=18$ . Solving this equation identifies the unknown whole.

Q2. A school reports that 42 students represent 35% of the students enrolled in a program. Without immediately calculating, which estimate is most reasonable for the total enrollment?

A.About 60

B.About 90

C.About 120 ✅

D.About 150

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: Because 35% is slightly more than one-third, the whole must be slightly less than three times 42. Three times 42 is 126, so an answer near 120 is reasonable. The other choices are inconsistent with the given percentage.

Q3. A store sells 24 notebooks, which is 20% of its original inventory. The manager wants to know the original number of notebooks. Which reasoning correctly determines the whole?

A.Divide 24 by

0.20

✅

B.Multiply 24 by

0.20

C.Subtract 20 from 24

D.Divide

0.20

by 24

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The known quantity, 24, is the part, while 20% is the fraction of the original inventory it represents. Therefore, the whole is found by dividing the part by the decimal form of the percent: $24\div0.20=120$ .

Q4. A teacher says, “If 16 students are 25% of the class, the class has 64 students.” A student claims the answer should be 20 because $16+25=41$ . Which explanation best evaluates the disagreement?

A.The teacher is correct because 25% means one-fourth of the whole ✅

B.The student is correct because percentages are added to the known part

C.Both are correct because they use different forms of the same equation

D.Neither is correct because the whole must always be larger than 100

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The teacher correctly interprets 16 as one-fourth of the whole because $25\%=0.25$ . Thus $16\div0.25=64$ . Adding a percentage value directly to a quantity mixes incompatible units and does not model the relationship.

Q5. A charity receives 72 donations from a campaign, and these donations are reported to be 45% of the campaign's total donations. What was the total number of donations?

A.120

B.150

C.160 ✅

D.180

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Let $x$ represent the total number of donations. The situation gives $0.45x=72$ . Dividing by $0.45$ gives $x=160$ . Checking confirms that 45% of 160 equals 72, so the model and result are consistent.

Q6. A nutrition label shows that 14 grams of a certain nutrient represent 35% of the daily amount. A student calculates $14\times35=490$ . What is the student's main modeling error?

A.The student treated 35% as 35 instead of

0.35

✅

B.The student should have added 35 to 14

C.The student should have divided 35 by 14

D.The student assumed the known amount was the whole

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: A percent must be converted to a decimal when it is used as a multiplication factor. Here, $35\%=0.35$ , so the equation is $0.35x=14$ . Using 35 instead produces a value that has no meaningful interpretation.

Q7. A graph shows four bars representing portions of different groups: Group A has 18 units at 30%, Group B has 24 units at 40%, Group C has 21 units at 35%, and Group D has 32 units at 50%. Which group has the largest whole?

A.Group A

B.Group B

C.Group C

D.Group D ✅

💡 Difficulty: hard | ✅ Correct: D

📖 Explanation: For each group, divide the known part by its percentage: A gives $18\div0.30=60$ , B gives $24\div0.40=60$ , C gives $21\div0.35=60$ , and D gives $32\div0.50=64$ . Therefore, Group D actually has the largest whole, making option D correct.

Q8. A company reports that 56 employees completed a training course, representing 70% of all employees assigned to the course. Another report says the total was 80 employees. How should the second report be evaluated?

A.It is correct because

56+24=80

B.It is correct because 70% of 80 equals 56 ✅

C.It is incorrect because 56 is greater than 70

D.It is incorrect because the total must be 126

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The report can be checked by calculating 70% of 80: $0.70(80)=56$ . Since this matches the reported number who completed the course, 80 is a valid whole. Verification through the original percentage relationship confirms the result.

Q9. A farmer has harvested 84 kilograms of tomatoes, which is 60% of the expected harvest. After finding the expected harvest, the farmer discovers that 15 kilograms were damaged. How many kilograms remain undamaged from the expected harvest?

A.111 ✅

B.125

C.126

D.140

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: First find the expected harvest using $0.60x=84$ , giving $x=140$ . Then subtract the 15 kilograms damaged: $140-15=125$ . Therefore, the correct result is 125 kilograms, not 111 or 126.

Q10. A graph indicates that 27 books represent 45% of a library section. A student estimates the whole as 50 books because 45% is close to one-half. Which evaluation is most accurate?

A.The estimate is reasonable because 27 is slightly more than half of 50

B.The estimate is too low because the whole should be 60 books ✅

C.The estimate is too high because the whole should be 45 books

D.The estimate cannot be evaluated without knowing the book titles

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: If 27 books are 45% of the whole, then $0.45x=27$ , giving $x=60$ . Also, 45% of 50 is only 22.5, not 27. The student's estimate is therefore too low and does not satisfy the percentage relationship.

Q11. A survey shows that 36 participants chose option X, representing 24% of all participants. A second survey has 15 more participants than the first. How many participants were in the second survey?

A.150

B.165 ✅

C.180

D.186

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The first survey's total is found from $0.24x=36$ , so $x=150$ . The second survey has 15 more participants, giving $150+15=165$ . This requires finding the original whole before applying the additional condition.

Q12. Two analysts solve the same problem: 63 units are 35% of a total. Analyst 1 calculates $63\div35=1.8$ . Analyst 2 calculates $63\div0.35=180$ . Which conclusion is best supported?

A.Analyst 1 is correct because percentages should remain whole numbers

B.Analyst 2 is correct because

35\%=0.35

and the result must be greater than the part ✅

C.Both analysts are correct because their answers differ only by notation

D.Neither is correct because finding a whole requires multiplication

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Analyst 2 correctly converts 35% to $0.35$ before dividing. The whole is $63\div0.35=180$ , and 180 is reasonable because 63 represents only 35% of it. Analyst 1's decimal answer results from treating the percent incorrectly.

🔗 Related Topics (MCQs)

📝 How Use a Problem Solving Strategy MCQs 📝 How to Approach word problems MCQs 📝 How to Use a problem solving strategy for word problems MCQs 📝 How to Solve number problems MCQs 📝 Translate English sentences into algebraic equations MCQs

←Previous Topic:Finding what percent one number is of another📝 Finding the Whole Given a Part and PercentFind percent increase:Next Topic→