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ISEE Middle Level Math : How to find a proportion

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Example Questions

Example Question #1 : How To Find A Proportion

For every $3 I earn at work, I donate $1 to charity. How much money will I donate if I make $27.00/week.

Possible Answers:

Correct answer:

Explanation:

To find the amount of the donation, divide 27 by 3.

$27\div 3=9$

The answer is 9.

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Example Question #2 : How To Find A Proportion

A Spanish class has $\small 14$ seniors and $\small 13$ juniors. What proportion of the class is juniors?

Possible Answers:

$\frac{13}{27}$

$\frac{13}{14}$

$\frac{14}{13}$

$\frac{14}{27}$

Correct answer:

$\frac{13}{27}$

Explanation:

A proportion is an amount that is part of a whole. There are $\small 27$ students in the class in total. This question asks for the proportion that are juniors. There are $\small 13$ juniors out of $\small 27$ students, therefore the proportion is:

$\frac{13}{27}$

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Example Question #1 : How To Find A Proportion

The distance between Youngston and Wynne is 240 miles in reality and three inches on a map. On the same map, Charlesville and Petersburg are one and three-fourths inches apart. How far apart are they in reality?

Possible Answers:

$120 \textrm{ mi}$

$140 \textrm{ mi}$

$144 \textrm{ mi}$

$128 \textrm{ mi}$

Correct answer:

$140 \textrm{ mi}$

Explanation:

240 real miles is represented by 3 map inches, making this a ratio of $240 \div 3 = 80$ real miles per map inch.

Therefore, one and three-fourths inches represents

$80 \times 1 \frac{3}{4} = \frac{80}{1} \times \frac{7}{4} = \frac{20}{1} \times \frac{7}{1} = 140$ miles, the distance between Charlesville and Petersburg.

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Example Question #3 : How To Find A Proportion

Read this problem, but do not solve it: Two inches on a map represent twenty-five miles of actual distance. If Pierce Springs and Buchanan Falls are eight inches apart on the map, how far apart are they in actuality?

If we let be the actual distance between Pierce Springs and Buchanan Falls, which proportion could be used to solve this problem?

Possible Answers:

$\frac{8}{N} = \frac{2}{25}$

$\frac{N}{25} = \frac{2}{8}$

$\frac{N}{25} = \frac{6}{8}$

$\frac{N}{8} = \frac{2}{25}$

$\frac{8}{N} = \frac{25}{2}$

Correct answer:

$\frac{8}{N} = \frac{2}{25}$

Explanation:

The ratios that are set equal to each other in a proportion must compare the same quantities in the same order.

In each ratio, we can put number of map inches in the numerator and the number of actual miles in the denominator.

One ratio is two map inches to twenty-five actual miles (the map scale); this ratio is $\frac{2}{25}$ .

The other ratio is eight map inches to actual miles (the distance between Pierce Springs and Buchanan Falls); this ratio is $\frac{8}{N}$ .

The proportion statement that sets these equal to each other is $\frac{8}{N} = \frac{2}{25}$ , and is therefore the correct choice.

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Example Question #3 : How To Find A Proportion

What is the value of x in $\frac{x+4}{x}=\frac{4}{12}?$

Possible Answers:

Correct answer:

Explanation:

Since this is a proportion, you can cross-multiply. Once you do that, the left side is 4x. Your right side is 12x+48 . Set those equal to each other. Then, combine like terms. Subtract 12x from both sides so that the equation is now -8x=48 . Divide both sides by -8. Your answer is -6.

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Example Question #1 : How To Find A Proportion

Michelle is having a party, and she is experimenting with different mixtures of soda, trying to come up with something original. In particular, she likes a drink she made when she mixed together three ounces of cola and five ounces of grape soda. She has two and a half liters of cola and wants to use it all to make some of this drink; how much grape soda does she need to mix it with?

Possible Answers:

$4 \frac{1}{6} \textrm{ L}$

$3 \frac{1}{6} \textrm{ L}$

$6 \textrm{ L}$

None of the other responses gives the correct answer.

$1\frac{1}{2} \textrm{ L}$

Correct answer:

$4 \frac{1}{6} \textrm{ L}$

Explanation:

The ratio of ounces of cola to ounces of grape soda in the initial mixture can be expressed as $\frac{3}{5}$ . It must be equal to that of liters of cola to liters of grape soda in the mixture Michelle will make for the party, which, since the number of liters of grape soda is unknown, is $\frac{2\frac{1}{2}}{N}$ . Set these equal and solve for :

$\frac{2\frac{1}{2}}{N} = \frac{3}{5}$

Set the cross-products equal to each other:

$3 N = 2\frac{1}{2} \cdot 5$

$3 N = \frac{5}{2} \cdot 5$

$3 N = \frac{25}{2}$

$\frac{1}{3} \cdot 3 N =\frac{1}{3} \cdot \frac{25}{2}$

$N = \frac{25}{6} = 4 \frac{1}{6}$

Michelle will use $4 \frac{1}{6}$ liters of grape soda in the final mixture.

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Example Question #7 : How To Find A Proportion

Robert, Jeff, and Paul are sharing a bag of chips that contains 20 chips. The three of them eat all of the chips. If Robert has eaten 8 chips, and Jeff eats twice as many chips as Paul, how many chips has Jeff eaten?

Possible Answers:

Correct answer:

Explanation:

What do we know? We know that there are 20 chips in the bag, and we know that Robert has eaten 8 of them. Thus, we can calculate that there are 20-8=12 chips remaining. Of this remaining, Jeff has eaten 2 parts and Paul has eaten 1 part: that's 3 parts, so let's calculate how many chips constitute each part:

$\frac{12}{3}=4$

So, each part is equal to 4 chips.

Jeff has eaten 2 parts, so 2*4=8 gives us our answer.

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Example Question #4 : How To Find A Proportion

If one cupcake costs 75 cents, how much does a dozen cupcakes cost?

Possible Answers:

$\$7.00$

$\$8.00$

$\$ 9.00$

$\$10.00$

Correct answer:

$\$ 9.00$

Explanation:

You can solve this problem using a proportion.

$\frac{1}{0.75}=\frac{12}{x}$

To solve for x, cross multiply.

$1\times x=12\times.75$

x=9.00

9 dollars

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Example Question #5 : How To Find A Proportion

If you can purchase two pairs of jeans for 50 dollars, how many pairs of jeans can you purchase with 200 dollars?

Possible Answers:

Correct answer:

Explanation:

You can use a proportion to solve this problem.

$\frac{2}{50}=\frac{x}{200}$

Cross multiply to solve for x.

$50\times x=200\times2$

50x =400

$400\div50 = 8$

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Example Question #4 : How To Find A Proportion

Phil earns $\$10.00$ for each hour he works. For every hour he works, he then gives $\$2.00$ to his sister Lola. How much money will Lola have if Phil works 13.5 hours?

Possible Answers:

$\$135.00$

$\$27.00$

$\$23.50$

$\$15.50$

$\$67.50$

Correct answer:

$\$27.00$

Explanation:

To Solve:

Multiply the $\$2.00$ Lola receives by the 13.5 hours Phil worked:

$\small $2.00 \cdot 13.5=27$

Phil will give Lola $\$27.00$ if he works 13.5 hours.

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ISEE Middle Level Math : How to find a proportion

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #1 : How To Find A Proportion

Example Question #2 : How To Find A Proportion

Example Question #1 : How To Find A Proportion

Example Question #3 : How To Find A Proportion

Example Question #3 : How To Find A Proportion

Example Question #1 : How To Find A Proportion

Example Question #7 : How To Find A Proportion

Example Question #4 : How To Find A Proportion

Example Question #5 : How To Find A Proportion

Example Question #4 : How To Find A Proportion

All ISEE Middle Level Math Resources

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