How to find the volume of a solution

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ACT Math › How to find the volume of a solution

Questions 1 - 6

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)?

100 mL

25 mL

150 mL

20 mL

50 mL

Explanation

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

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

Explanation

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

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

Now, solving for , you get:

Be careful, though! This means that the total solution is actually or .

A dog eats treats in days. At this rate, how many treats does the dog eat in days?

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

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

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

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

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

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 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 $\frac {9}{4}$ treats a day.

Then we multiply that number by the number of days.

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

Now simplify.

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

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

$384\textup{ml}$

$144\textup{ml}$

$158\textup{ml}$

$504\textup{ml}$

$424\textup{ml}$

Explanation

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

$\frac{3}{5}$

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:

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

Solving for X, you get:

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:

or $384\textup{ml}$

There is a coffee drink made of of coffee, of milk, of cream, and of flavoring. If you have an unlimited amount of flavoring and milk but only of cream and of coffee, how many ounces of drink can you make? (Presume that you cannot make partial servings.)

Explanation

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

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

For the coffee, you can make:

$\frac{450}{4}=112.5$ 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 . If you can make servings (remember, no partial servings!), you can make a total of .

One serving of party drink is comprised of of syrup, of water, and of apple juice. If a large bowl of the drink contains of apple juice, how much of the total drink is in the bowl?