Answer:
The amount of sugar needed to make 1 quart of lemonade is <u>1/12 cup</u>.
Step-by-step explanation:
Given:
Alex made 4 quarts of lemonade using 1/3 cup of sugar.
Now, to determine the amount of sugar needed to make 1 quart of lemonade.
Let the amount of sugar needed to make 1 quart of lemonade =
.
So, by using the proportion we solve it:
![\frac{quarts\ of \ lemonade}{cup\ of\ sugar} =\frac{quart\ of\ lemonade}{cup\ of\ sugar}](https://tex.z-dn.net/?f=%5Cfrac%7Bquarts%5C%20of%20%5C%20lemonade%7D%7Bcup%5C%20of%5C%20sugar%7D%20%3D%5Cfrac%7Bquart%5C%20of%5C%20lemonade%7D%7Bcup%5C%20of%5C%20sugar%7D)
![\frac{4}{\frac{1}{3}} =\frac{1}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%3D%5Cfrac%7B1%7D%7Bx%7D)
<em>On solving we get:</em>
![x=\frac{\frac{1}{3}}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B3%7D%7D%7B4%7D)
![x=\frac{1}{12}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B12%7D)
So, cup of sugar = ![\frac{1}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B12%7D)
Therefore, the amount of sugar needed to make 1 quart of lemonade is 1/12 cup.