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ACT Math : How to find the volume of a solution

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Example Questions

Example Question #1 : Proportion / Ratio / Rate

A rectangular container holds a liquid. The dimensions of the container are 5 cm by 5 cm by 4 cm. If the container is half full, how much liquid is in the container (1 cm³= 1mL)?

Possible Answers:

20 mL

25 mL

150 mL

100 mL

50 mL

Correct answer:

50 mL

Explanation:

The total volume is 5 * 5 * 4 = 100 cm³. Half of this is 50 cm³which is 50 mL.

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Example Question #2 : Proportion / Ratio / Rate

A dog eats $\displaystyle 9$ treats in $\displaystyle 4$ days. At this rate, how many treats does the dog eat in 4+x $\displaystyle 4+x$ days?

Possible Answers:

$\frac{9}{4}+\frac{x}{4}$ $\displaystyle \frac{9}{4}+\frac{x}{4}$

$\frac{9}{4}+4x$ $\displaystyle \frac{9}{4}+4x$

$\frac{9}{4}+\frac{9x}{4}$ $\displaystyle \frac{9}{4}+\frac{9x}{4}$

$9+\frac{9x}{4}$ $\displaystyle 9+\frac{9x}{4}$

$9+\frac{x}{4}$ $\displaystyle 9+\frac{x}{4}$

Correct answer:

$9+\frac{9x}{4}$ $\displaystyle 9+\frac{9x}{4}$

Explanation:

This is a rate problem. We need to first find out how many treats a day the dog eats. Then to find the number of treats the dog eats in 4+x $\displaystyle 4+x$ days, we multiply the number of days by the number of treats a day the dog eats.

From the given information, we know that the dog eats $\frac {9}{4}$ $\displaystyle \frac {9}{4}$ treats a day.

Then we multiply that number by the number of days.

$\frac{9}{4}(4+x)$ $\displaystyle \frac{9}{4}(4+x)$

Now simplify.

$9+\frac{9x}{4}$ $\displaystyle 9+\frac{9x}{4}$

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Example Question #1 : How To Find The Volume Of A Solution

One serving of party drink is comprised of $3\:oz$ $\displaystyle 3\:oz$ of syrup, $4\:oz$ $\displaystyle 4\:oz$ of water, and $3\:oz$ $\displaystyle 3\:oz$ of apple juice. If a large bowl of the drink contains $237\:oz$ $\displaystyle 237\:oz$ of apple juice, how much of the total drink is in the bowl?

Possible Answers:

$790\:oz$ $\displaystyle 790\:oz$

$2730\:oz$ $\displaystyle 2730\:oz$

$313\:oz$ $\displaystyle 313\:oz$

$553\:oz$ $\displaystyle 553\:oz$

$79\:oz$ $\displaystyle 79\:oz$

Correct answer:

$790\:oz$ $\displaystyle 790\:oz$

Explanation:

The total drink is made up of $3+4+3=10\:oz$ $\displaystyle 3+4+3=10\:oz$. Therefore, for a problem like this, you can set up a ratio:

$\frac{x}{10}=\frac{237}{3}$ $\displaystyle \frac{x}{10}=\frac{237}{3}$

First, simplify the right side of the equation:

$\frac{x}{10}=79$ $\displaystyle \frac{x}{10}=79$

Next, solve for $\displaystyle x$:

x=790 $\displaystyle x=790$. Therefore, the total amount of drink is $790\:oz$ $\displaystyle 790\:oz$.

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Example Question #2 : Proportion / Ratio / Rate

There is a coffee drink made of $4\:oz$ $\displaystyle 4\:oz$ of coffee, $3\:oz$ $\displaystyle 3\:oz$ of milk, $2.5\:oz$ $\displaystyle 2.5\:oz$ of cream, and $1\:oz$ $\displaystyle 1\:oz$ of flavoring. If you have an unlimited amount of flavoring and milk but only $350\:oz$ $\displaystyle 350\:oz$ of cream and $450\:oz$ $\displaystyle 450\:oz$ of coffee, how many ounces of drink can you make? (Presume that you cannot make partial servings.)

Possible Answers:

$225.25\:oz$ $\displaystyle 225.25\:oz$

$1384.15\:oz$ $\displaystyle 1384.15\:oz$

$1050\:oz$ $\displaystyle 1050\:oz$

$1176\:oz$ $\displaystyle 1176\:oz$

$1181.25\:oz$ $\displaystyle 1181.25\:oz$

Correct answer:

$1176\:oz$ $\displaystyle 1176\:oz$

Explanation:

To begin with, you need to compute what is going to be your limiting factor. For the cream, you can make:

$\frac{350}{2.5}=140$ $\displaystyle \frac{350}{2.5}=140$ servings.

For the coffee, you can make:

$\frac{450}{4}=112.5$ $\displaystyle \frac{450}{4}=112.5$ servings.

Therefore, this second value is your total number of servings. (You must choose the minimum, for it will be what limits your beverage-making.)

So, you know that each drink is $4+3+2.5+1=10.5\:oz$ $\displaystyle 4+3+2.5+1=10.5\:oz$. If you can make 112 $\displaystyle 112$ servings (remember, no partial servings!), you can make a total of $112*10.5=1176\:oz$ $\displaystyle 112*10.5=1176\:oz$.

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Example Question #5 : Proportion / Ratio / Rate

A drink is made up of $4\textup{ parts}$ $\displaystyle 4\textup{ parts}$ orange juice to $7\textup{ parts}$ $\displaystyle 7\textup{ parts}$ carbonated water. If a bowl of this drink contains $161\textup{ cups}$ $\displaystyle 161\textup{ cups}$ of carbonated water, how many total cups of the drink are there in the bowl?

Possible Answers:

$\displaystyle 92$

442.75 $\displaystyle 442.75$

184 $\displaystyle 184$

281.75 $\displaystyle 281.75$

253 $\displaystyle 253$

Correct answer:

253 $\displaystyle 253$

Explanation:

To start this, you can set up a proportion as follows:

$\frac{4}{7}=\frac{x}{161}$ $\displaystyle \frac{4}{7}=\frac{x}{161}$, where $\displaystyle x$ is the number of cups of orange juice.

Now, solving for $\displaystyle x$, you get:

x=92 $\displaystyle x=92$

Be careful, though! This means that the total solution is actually 92+161 $\displaystyle 92+161$ or 253 $\displaystyle 253$.

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Example Question #6 : Proportion / Ratio / Rate

A solution has $30\textup{ ml}$ $\displaystyle 30\textup{ ml}$ of solution X and $50\textup{ ml}$ $\displaystyle 50\textup{ ml}$ of solution Y. If you wanted a solution containing $240\textup{ ml}$ $\displaystyle 240\textup{ ml}$ of solution Y, how much total solution would you need?

Possible Answers:

$144\textup{ml}$ $\displaystyle 144\textup{ml}$

$158\textup{ml}$ $\displaystyle 158\textup{ml}$

$504\textup{ml}$ $\displaystyle 504\textup{ml}$

$384\textup{ml}$ $\displaystyle 384\textup{ml}$

$424\textup{ml}$ $\displaystyle 424\textup{ml}$

Correct answer:

$384\textup{ml}$ $\displaystyle 384\textup{ml}$

Explanation:

To start, notice that the ratio of solution X to solution Y is:

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

Based on the quesiton, you know that you are looking for a certain amount of solution X based on a given amount of solution Y. Thus, for your data, you know:

$\frac{3}{5}=\frac{x}{240}$ $\displaystyle \frac{3}{5}=\frac{x}{240}$

Solving for X, you get:

x=144 $\displaystyle x=144$

This is the total amount of solution X that you will need to keep the ratios correct. Do not forget that you need to have a total solution amount, thus add this amount of solution X to solution Y's amount, thus giving you:

$\displaystyle 144 + 240$ or $384\textup{ml}$ $\displaystyle 384\textup{ml}$

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ACT Math : How to find the volume of a solution

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Proportion / Ratio / Rate

Example Question #2 : Proportion / Ratio / Rate

Example Question #1 : How To Find The Volume Of A Solution

Example Question #2 : Proportion / Ratio / Rate

Example Question #5 : Proportion / Ratio / Rate

Example Question #6 : Proportion / Ratio / Rate

All ACT Math Resources

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