Elyse and Jamir each make fruit punch. Elyse mixes 1

5
4

cups of water with
4
3

cups of fruit punch mix. Jamir mixes 1
3
1

cups of water with
9
8

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
5
4

cups of water by to find 1 cup of water?
Elyse's Fruit Punch Recipe
÷
Water
(cups) Fruit Punch Mix
(cups)
1
5
4


4
3


1 ?

1 answer

To find the number of cups of fruit punch mix per 1 cup of water in Elyse’s recipe, we need to convert the mixed quantities into improper fractions and then find the unit rate.

Step 1: Convert to Improper Fractions

  1. Water:

    • \(1 \frac{5}{4} = 1 + \frac{5}{4} = \frac{4}{4} + \frac{5}{4} = \frac{9}{4}\) cups of water.
  2. Fruit Punch Mix:

    • \(4 \frac{3}{4} = 4 + \frac{3}{4} = \frac{16}{4} + \frac{3}{4} = \frac{19}{4}\) cups of fruit punch mix.

Step 2: Calculate the Unit Rate

To find out how many cups of fruit punch mix there are per 1 cup of water, we divide the amount of fruit punch mix by the amount of water:

\[ \text{Unit Rate} = \frac{\text{Fruit Punch Mix (cups)}}{\text{Water (cups)}} = \frac{\frac{19}{4}}{\frac{9}{4}} = \frac{19}{4} \times \frac{4}{9} = \frac{19}{9} \]

This means Elyse's recipe has \(\frac{19}{9}\) cups of fruit punch mix for every 1 cup of water.

Step 3: Repeat for Jamir's Recipe

Now let's calculate Jamir's recipe in the same way.

  1. Water:

    • \(1 \frac{3}{1} = 1 + 3 = 4\) cups of water.
  2. Fruit Punch Mix:

    • \(9 \frac{8}{1} = 9 + 8 = 17\) cups of fruit punch mix.

Now calculating the unit rate:

\[ \text{Unit Rate} = \frac{17}{4} \div 4 = \frac{17}{4} \times \frac{1}{4} = \frac{17}{16} \]

Comparing the Unit Rates

  • Elyse's fruit punch mix per 1 cup of water: \(\frac{19}{9}\)
  • Jamir's fruit punch mix per 1 cup of water: \(\frac{17}{16}\)

To compare these, we can convert them to decimals:

  1. \( \frac{19}{9} \approx 2.11\)
  2. \( \frac{17}{16} = 1.0625\)

Conclusion

Elyse’s fruit punch is fruitier than Jamir’s, as she has a higher unit rate of fruit punch mix to water in her recipe.