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.



Priya needs 13⅓ cups of orange juice

Diego 15 cups

Step-by-step 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

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b