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Algebra 1 : Whole and Part

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1 : How To Find The Whole From The Part With Percentage

70% of a quantity is 35. What is the quantity?

Possible Answers:

24.5 $\displaystyle 24.5$

45.5 $\displaystyle 45.5$

$\displaystyle 50$

$\displaystyle 42$

44.5 $\displaystyle 44.5$

Correct answer:

$\displaystyle 50$

Explanation:

We can write this as an equation:

$0.70\cdot x=35$ $\displaystyle 0.70\cdot x=35$

$x=\frac{35}{0.7}$ $\displaystyle x=\frac{35}{0.7}$

x=50 $\displaystyle x=50$

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Example Question #2 : Whole And Part

80% of ____ = 72?

Possible Answers:

$\displaystyle 80$

$\displaystyle 88$

$\displaystyle 94$

$\displaystyle 90$

$\displaystyle 86$

Correct answer:

$\displaystyle 90$

Explanation:

$\frac{80}{100}=\frac{4}{5}$ $\displaystyle \frac{80}{100}=\frac{4}{5}$

$\frac{4}{5}x=72$ $\displaystyle \frac{4}{5}x=72$

Divide by fractions:

$x=\frac{5}{4}\cdot 72=90$ $\displaystyle x=\frac{5}{4}\cdot 72=90$

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Example Question #2 : How To Find The Whole From The Part With Percentage

Malcolm spent 15% of his money on a bicycle that costs $300. How many dollars does Malcolm have left?

Possible Answers:

1700 $\displaystyle 1700$

1600 $\displaystyle 1600$

1500 $\displaystyle 1500$

2000 $\displaystyle 2000$

1800 $\displaystyle 1800$

Correct answer:

1700 $\displaystyle 1700$

Explanation:

If $300 was 15% of Malcolm's money, then we can figure out how much money Malcolm had by creating this equation:

$\displaystyle .15x=300$

In this case, Malcolm had $2,000. Since he spent $300 of it on a bicycle, he has only $1,700 left.

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Example Question #3 : How To Find The Whole From The Part With Percentage

If 45 is 15% of $\displaystyle x$ , find the value of $\displaystyle x$ .

Possible Answers:

$\displaystyle 30$

275 $\displaystyle 275$

300 $\displaystyle 300$

450 $\displaystyle 450$

33.3 $\displaystyle 33.3$

Correct answer:

300 $\displaystyle 300$

Explanation:

The key to this problem is identifying that "15% of $\displaystyle x$ " is the same as 0.15x $\displaystyle 0.15x$ . With this information, we can write out the simple equation

$\displaystyle 45=0.15x$

Dividing both sides by 0.15 $\displaystyle 0.15$ gives us

x=300 $\displaystyle x=300$

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Example Question #4 : How To Find The Whole From The Part With Percentage

$1\tfrac{1}{2}$ $\displaystyle 1\tfrac{1}{2}$ % of what number is 900?

Possible Answers:

13,500 $\displaystyle 13,500$

60,000 $\displaystyle 60,000$

12,000 $\displaystyle 12,000$

120,000 $\displaystyle 120,000$

135,000 $\displaystyle 135,000$

Correct answer:

60,000 $\displaystyle 60,000$

Explanation:

$1\tfrac{1}{2}$ $\displaystyle 1\tfrac{1}{2}$ % of a number, or, equivalently, 1.5% of a number, is the same as 0.015 multiplied by that number. If we call that number $\displaystyle x$ , then

$\displaystyle 0.015x=900$

$x = 900\div 0.015 = 60,000$ $\displaystyle x = 900\div 0.015 = 60,000$

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Example Question #6 : How To Find The Whole From The Part With Percentage

Dana spent 24% of her savings on a laptop that costs $900. How much savings does she have left?

Possible Answers:

3250 $\displaystyle 3250$

3750 $\displaystyle 3750$

2850 $\displaystyle 2850$

3550 $\displaystyle 3550$

4500 $\displaystyle 4500$

Correct answer:

2850 $\displaystyle 2850$

Explanation:

We know that prior to her purchase, $900 was 24% of Dana's Savings. Therefore, Dana's total savings prior to her purchase can be modeled as $\displaystyle 0.24x=900$ , where $\displaystyle x$ is Dana's total savings. Solving for $\displaystyle x$ would give you x=3750 $\displaystyle x=3750$ , which indicates that Dana's savings was $3750 prior to her purchase. After her purchase, she will have $2850 left.

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Example Question #6 : Whole And Part

There are 36 blue marbles in a bag. If blue marbles made up 24% of the marbles in the bag, what is the total number of marbles are in the bag?

Possible Answers:

144 $\displaystyle 144$

148 $\displaystyle 148$

150 $\displaystyle 150$

152 $\displaystyle 152$

Correct answer:

150 $\displaystyle 150$

Explanation:

If $\displaystyle x$ is the total number of marbles in the bag, then $\displaystyle 0.24x=36$ , since 24% of marbles in the bag are blue and there are 36 marbles. Solving for this equation will give you x=150 $\displaystyle x=150$ , which means there must be a total of 150 marbles in the bag.

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Example Question #3 : Whole And Part

12% of the students at a certain high school have perfect attendance. If 27 students have perfect attendance, how many total students does the school contain?

Possible Answers:

248 $\displaystyle 248$

550 $\displaystyle 550$

180 $\displaystyle 180$

225 $\displaystyle 225$

300 $\displaystyle 300$

Correct answer:

225 $\displaystyle 225$

Explanation:

From the given information here, we know that 12% of the total number equals 27. Mathematically, if we use $\displaystyle x$ to represent the total that we are looking for, we can write this as

$\displaystyle (0.12)(x)=27$

The next step is dividing both sides by 0.12 $\displaystyle 0.12$ .

$\frac{27}{0.12}=225$ $\displaystyle \frac{27}{0.12}=225$

so there are 225 students in the school.

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Example Question #3 : How To Find The Whole From The Part With Percentage

$\displaystyle 4$ is $48\%$ $\displaystyle 48\%$ of what?

Possible Answers:

$\small 1.2$ $\displaystyle \small 1.2$

$\small 1.92$ $\displaystyle \small 1.92$

$\displaystyle 12$

$\small 0.08\overline{3}$ $\displaystyle \small 0.08\overline{3}$

$\small 8.\overline{3}$ $\displaystyle \small 8.\overline{3}$

Correct answer:

$\small 8.\overline{3}$ $\displaystyle \small 8.\overline{3}$

Explanation:

To figure out the value, translate the question into an equation, knowing that "is" means equals, and "of" means multiply:

$\small 4 = 48\%*x$ $\displaystyle \small 4 = 48\%*x$

To solve, turn the percentage into a decimal:

$\small 4=0.48*x$ $\displaystyle \small 4=0.48*x$ now divide both sides by 0.48

$\small 8.\overline{3}=x$ $\displaystyle \small 8.\overline{3}=x$

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Example Question #9 : How To Find The Whole From The Part With Percentage

$\displaystyle 10$ is $180\%$ $\displaystyle 180\%$ of what number?

Possible Answers:

0.18 $\displaystyle 0.18$

$\small 1.8$ $\displaystyle \small 1.8$

$\small 5.\overline{5}$ $\displaystyle \small 5.\overline{5}$

$\small 55.\overline{5}$ $\displaystyle \small 55.\overline{5}$

$\displaystyle 18$

Correct answer:

$\small 5.\overline{5}$ $\displaystyle \small 5.\overline{5}$

Explanation:

To determine the whole, translate the question into an equation, knowing that "is" means equals and "of" means multiply:

$\small 10 = 180\%*x$ $\displaystyle \small 10 = 180\%*x$ convert the percentage into a decimal:

$\small 10 = 1.8*x$ $\displaystyle \small 10 = 1.8*x$ divide both sides by 1.8

$\small 5.\overline{5}=x$ $\displaystyle \small 5.\overline{5}=x$

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Algebra 1 : Whole and Part

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find The Whole From The Part With Percentage

Example Question #2 : Whole And Part

Example Question #2 : How To Find The Whole From The Part With Percentage

Example Question #3 : How To Find The Whole From The Part With Percentage

Example Question #4 : How To Find The Whole From The Part With Percentage

Example Question #6 : How To Find The Whole From The Part With Percentage

Example Question #6 : Whole And Part

Example Question #3 : Whole And Part

Example Question #3 : How To Find The Whole From The Part With Percentage

Example Question #9 : How To Find The Whole From The Part With Percentage

All Algebra 1 Resources

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