Question

A store sells two different brands of lemonade mix. For Brand A, one-half cup of mix makes a pitcher. For Brand B, one-fourth cup of mix makes a pitcher. The container for Brand A contains 4 more cups of mix than the container for Brand B. Both containers make the same number of pitchers of lemonade.



How many pitchers of lemonade can each container make? Enter the answer in the box.

Response area with 1 text input box
pitchers

Answer 1

Let \( x \) be the number of cups of mix in the container for Brand B. Therefore, the container for Brand A will have \( x + 4 \) cups of mix.

Brand A requires \( \frac{1}{2} \) cup of mix per pitcher, so the number of pitchers it can make is:

\[
\frac{x + 4}{\frac{1}{2}} = 2(x + 4) = 2x + 8
\]

Brand B requires \( \frac{1}{4} \) cup of mix per pitcher, so the number of pitchers it can make is:

\[
\frac{x}{\frac{1}{4}} = 4x
\]

Since both containers make the same number of pitchers, we can set the two expressions equal to one another:

\[
2x + 8 = 4x
\]

Now, we'll solve for \( x \):

\[
8 = 4x - 2x
\]
\[
8 = 2x
\]
\[
x = 4
\]

So, the container for Brand B has 4 cups of mix. Now we can find the amount of mix in Brand A:

\[
x + 4 = 4 + 4 = 8 \text{ cups}
\]

Now, we can calculate the number of pitchers each brand can make:

For Brand A:
\[
\text{Pitchers} = \frac{8}{\frac{1}{2}} = 16
\]

For Brand B:
\[
\text{Pitchers} = \frac{4}{\frac{1}{4}} = 16
\]

Thus, both containers can make the same number of pitchers:

\[
\text{Pitchers} = 16
\]

Therefore, the answer is:

**16**