Priya mixes 2 ½ cups of water with ⅓ cup of orange juice concentrate. Diego mixes 1 ⅔ cups of water with ¼ cup orange juice concentrate.
How much concentrate should Diego mix with 100 cups of water to make juice that tastes the same as the original recipe?
If necessary round your answer to the nearest hundredth.
To find out how much concentrate Diego should mix with 100 cups of water, we need to set up a proportion using the ratio of water to concentrate from the original recipe.
For Priya's recipe:
Water: 2 ½ cups
Concentrate: ⅓ cup
For Diego's recipe:
Water: 1 ⅔ cups
Concentrate: ¼ cup
To find the ratio of water to concentrate, we can divide the water by the concentrate for each recipe:
Priya's ratio: 2 ½ cups / ⅓ cup = (2.5)/(0.33) ≈ 7.58
Diego's ratio: 1 ⅔ cups / ¼ cup = (1.67)/(0.25) = 6.68
So, the ratio of water to concentrate should be approximately 7.58 for them to taste the same.
Now, let's set up a proportion to find out how much concentrate Diego should mix with 100 cups of water:
Water: 100 cups
Concentrate: x cups
The ratio of water to concentrate should be approximately 7.58.
So, we can set up the proportion:
100 cups / x cups = 7.58
Cross-multiplying, we get:
100 * 7.58 = x
x ≈ 758
Therefore, Diego should mix approximately 758 cups of orange juice concentrate with 100 cups of water to make juice that tastes the same as the original recipe.