Question

Elyse and Jamir each make fruit punch. Elyse mixes 1
2
1
​
cups of water with
8
1
​
cups of fruit punch mix. Jamir mixes 1
5
3
​
cups of water with
3
1
​
cups of fruit punch mix. Which fruit punch has a fruitier taste?
Start by finding the unit rate for Elyse’s recipe. You need to find the number of cups of fruit punch mix per 1 cup of water. What can you divide 1
2
1
​
cups of water by to find 1 cup of water?
Elyse's Fruit Punch Recipe
÷
1

1
2
Water
(cups) Fruit Punch Mix
(cups)
1
2
1
​

8
1
​

1 ?
Great job!
To keep the ratio equivalent, you need to divide
8
1
​
by 1
2
1
​
also. How many cups of fruit punch mix does Elyse’s recipe need for 1 cup of water? Solve
8
1
​
÷ 1
2
1
​
on paper, then enter your answer on Zearn.
Elyse's Fruit Punch Recipe
÷ 1
2
1
​

÷ 1
2
1
​

Water
(cups) Fruit Punch Mix
(cups)
1
2
1
​

8
1
​

1

Answer 1

To find the unit rate for Elyse’s recipe, we need to determine how many cups of fruit punch mix correspond to 1 cup of water. Elyse uses \( \frac{1}{2} \frac{1}{1} \) cups of water and \( \frac{8}{1} \) cups of fruit punch mix.

1. **Convert the mixed numbers to improper fractions:**
- For water: \( \frac{1}{2} \frac{1}{1} = \frac{3}{2} \) (since \( 1 = \frac{2}{2} \) and \( \frac{1}{2} + \frac{2}{2} = \frac{3}{2} \))
- For fruit punch mix: \( \frac{8}{1} = 8 \)

2. **Set up the division:**
We need to divide the amount of fruit punch mix by the amount of water:
\[
\text{Fruit punch mix per 1 cup of water} = \frac{8}{\frac{3}{2}} = 8 \times \frac{2}{3} = \frac{16}{3}
\]

Thus, Elyse’s mix has \( \frac{16}{3} \) cups of fruit punch mix per 1 cup of water.

Next, we will find the unit rate for Jamir’s recipe.

1. **Convert the mixed numbers to improper fractions:**
- For water: \( \frac{1}{5} \frac{3}{1} = \frac{8}{5} \) (where \( 3 = \frac{15}{5} \) and \( \frac{1}{5} + \frac{15}{5} = \frac{16}{5} \))
- For fruit punch mix: \( \frac{3}{1} = 3 \)

2. **Set up the division:**
We need to divide the amount of fruit punch mix by the amount of water:
\[
\text{Fruit punch mix per 1 cup of water} = \frac{3}{\frac{8}{5}} = 3 \times \frac{5}{8} = \frac{15}{8}
\]

Now we can compare the results:
- Elyse's fruit punch has \( \frac{16}{3} \) cups of fruit punch mix per cup of water.
- Jamir's fruit punch has \( \frac{15}{8} \) cups of fruit punch mix per cup of water.

Now we need to convert these fractions into decimals to compare them:
- \( \frac{16}{3} \approx 5.33 \)
- \( \frac{15}{8} = 1.875 \)

Thus, Elyse's fruit punch is significantly fruitier than Jamir's fruit punch.