Question

Priya mixes 2 1/2 cups of water with 1/3 cup of orange juice concentrate. Diego mixes 1 2/3 cups of water with 1/4 cup orange juice concentrate. How much concentrate should each of them mix with 100 cups of water to make juice that tastes the same as their original recipe? Explain or show your reasoning.

Answer 1

Answer:

Priya needs 13⅓ cups of orange juice

Diego 15 cups

Explanation:

......................................................................................................................

Priya

......................................................................................................................

Cup of water = 2½

Cup of orange = ⅓

If 2½ cups of water requires ½ cup of orange juice concentrate

Then 100 cups of water would require x cup of orange

Representing the above statement mathematically

2½ : ⅓ = 100 : x

5/2 : 1/3 = 100 : x ------------------Convert ratio sign to division

5/2 ÷⅓ = 100/x

5/2 * 3 = 100/x

15/2 = 100/x ---------------Multiply both sides by x

15/2 * x = 100/x * x

15x/2 = 100 ------------------ Multiply both sides by 2

2 * 15x/2 = 2 * 100

15x = 200 --------------- Divide both sides by 15

x = 200/15

x = 13⅓

So, 13⅓ cups of orange is needed by Priya

......................................................................................................................

Diego

......................................................................................................................

Cup of water = 1⅔

Cup of orange = ¼

If 1⅔ cups of water requires ¼ cup of orange juice concentrate

Then 100 cups of water would require x cup of orange

Representing the above statement mathematically

1⅔:¼ = 100:x

5/3 : ¼ = 100:x

5/3 ÷¼ = 100 ÷ x

5/3 * 4/1 = 100 ÷ x

20/3 =100/x----------------------- Multiply x to both sides

20/3 * x = 100/x * x

20x/3 = 100 ------------------------ Multiply 3 to sides by 3

3 * 20x/3 = 100 * 3

20x = 300 ------------- Divide both sides by 2

20x/20 = 300/20

x = 15

So, 15 cups of orange is needed by Diego