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## 5. Priya mixes 2..5 cups of water with 1/3 cup or orange juice concentrate. Diego mixes 1 2/3 cups of water with 1/4 cup or orange concentra

Question

5. Priya mixes 2..5 cups of water with 1/3 cup or orange juice concentrate. Diego mixes 1 2/3 cups of water with 1/4 cup or orange concentrate. How much concentrate should Diego mix with 100 cups of water to make juice that tastes the same as their original recipe?

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Mathematics
5 months
2021-08-09T06:24:12+00:00
2021-08-09T06:24:12+00:00 1 Answers
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## Answers ( )

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