How to find a ratio - ISEE Lower Level Quantitative Reasoning

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Question

Cassie works a four hour shift at the coffee shop. During her shift, $\small 37$ customers order coffee, $\small 27$ order orange juice, and $\small 15$ order hot choclate. What is the ratio of customers who order orange juice to those who order coffee?

Answer

Since there are $\small 27$ customers who order orange juice, $\small 27$ is the first number of our ratio.

The second number of our ratio is $\small 37$ , because $\small 37$ people order coffee.

Therefore, our ratio is :

$\small 27:37$

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Question

Stacy has started collecting coins. She has twice as many wheat pennies as she does 1946 dimes, and three times as many 1983 quarters as she does 1946 dimes. If Stacy has $\small 4$ 1946 dimes, what is the ratio of wheat pennies to 1983 quarters?

Answer

We know that Stacy has $\small 4$ 1946 dimes.

We also know that she has twice as many wheat pennies, so we must multiply $\small 4$ by $\small 2$ to find the total number of wheat pennies.

$\small 4\cdot 2=8$

We also know that Stacy has three times as many 1986 quarters, so we multiply $\small 4$ by $\small 3$ to find the total number of 1986 quarters.

$\small 4\cdot 3=12$

Now our ratio of wheat pennies to 1986 quarters is $\small 8:12$ , but this can be simplified because both numbers are divisible by $\small 4$ .

$\small (8/4)=2$

$\small (12/4)=3$

So our ratio becomes $\small 2:3$

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Question

Steve is having a birthday party. So far, he has invited thirty-nine of his friends from school, fifteen of whom are girls. He wants to make the ratio of girls to boys at the party two to one. How many more girls does he need to invite, assuming no more boys are invited?

Answer

Counting Steve, there are forty attendees so far, fifteen of whom are girls and twenty-five of whom (including Steve) are boys. To obtain a two-to-one girl to boy ratio, he needs to invite a total of fifty girls, so he needs to invite thirty-five more.

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Question

For every 3 peanuts in a bag of trail mix, there are 1 chocolate chip and 2 raisins. What is the proportion of raisins in the mix?

Answer

Given that there are 3 peanuts for every 1 chocolate chip and 2 raisins, the proportion of raisins can be found by dividing the number of raisins by the sum of all the items in the mix. This results in:

$\frac{2}{3+1+2}=\frac{2}{6}=\frac{1}{3}$ .

Therefore, $\frac{1}{3}$ is the correct answer.

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Question

Scott's mother bakes 12 cookies and he eats half of them. Scott's mom then puts red frosting on 4 cookies and blue frosting on the rest of the cookies. What is the ratio of cookies with red frosting to cookies with blue frosting?

Answer

If Scott's mother bakes 12 cookies and he eats half of them, that means he will eat 6 cookies, leaving 6 uneaten cookies.

If Scott's mom then puts red frosting on 4 cookies and blue frosting on the rest of the cookies, 2 cookies will get blue frosting. ().

Therefore, the ratio of cookies with red frosting to cookies with blue frosting is , which is equal to .

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Question

Jose is times taller than his baby brother Michael. If Jose is inches tall, how tall is Michael?

Answer

The ratio of Jose to Michael's height is .

Thus, if Jose is inches taller than Michael must be times shorter.

We can write this as the expression, $\frac{48}{3}=16$ .

Also, an equivalent ratio for = .

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Question

Find an equivalent ratio.

Answer

An equivalent ratio of is .

This is the furthest simplification of the ratio.
The greatest common divisor is needed to simplify the expression.

Both and are divisible by , $\frac{15}{3}=5$ and $\frac{3}{3}=1$ .

Thus, the correct answer is .

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Question

Solve for .

Answer

To solve this problem the relationship between the two numbers in the first ratio needs to be established.

Since, is times larger than , an equivalent ratio must have the same relationship.

Thus, must be times larger than , and $19\cdot 3=57$

Thus,

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Question

There are students in a fifth grade class. If there are girls in the class, what is the ratio of the number of boys in the class to the total number of students in the class?

Answer

First, find the number of boys in the class by subtracting the number of girls in the class from the total number of students.

$\text{Number of boys}=36-12=24$

Now, we know that the ratio of the number of boys in the class to the total number of students in the class is $24\text{ to }36$ .

We can express that ratio as the following fraction:

$\frac{24}{36}=\frac{2}{3}$

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Question

There are students in a computer science class. If there are boys in the class, what is the ratio of the number of girls in the class to the total number of students in the class?

Answer

First, find the number of girls in the class by subtracting the number of boys in the class from the total number of students.

$\text{Number of girls}=40-15=25$

Now, we know that the ratio of the number of boys in the class to the total number of students in the class is $25\text{ to }40$ .

We can express that ratio as the following fraction:

$\frac{25}{40}=\frac{5}{8}$

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Question

In a litter of puppies, there are black puppies and white puppies. What is the ratio of the number of white puppies to black puppies?

Answer

The ratio wants us to compare the number of white puppies to the number of black puppies.

We can say the ratio of white puppies to black puppies is $8\text{ to } 4$ . When we write that as a fraction, it becomes $\frac{8}{4}=\frac{2}{1}$ , so we can also say that the ratio of white puppies to black puppies is $2\text{ to }1$ or .

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Question

Stacy has started collecting coins. She has twice as many wheat pennies as she does dimes, and three times as many quarters as she does dimes. If Stacy has $\small 4$ dimes, what is the ratio of wheat pennies to quarters?

Answer

We know that Stacy has $\small 4$ 1946 dimes.

We also know that she has twice as many wheat pennies, so we must multiply $\small 4$ by $\small 2$ to find the total number of wheat pennies.

$\small 4\cdot 2=8$

We also know that Stacy has three times as many 1986 quarters, so we multiply $\small 4$ by $\small 3$ to find the total number of 1986 quarters.

$\small 4\cdot 3=12$

Now our ratio of wheat pennies to 1986 quarters is $\small 8:12$ , but this can be simplified because both numbers are divisible by $\small 4$ .

$\small (8/4)=2$

$\small (12/4)=3$

So our ratio becomes $\small 2:3$

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