Priya needs 13⅓ cups of orange juice
Diego 15 cups
Step-by-step explanation:
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Priya
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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
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Diego
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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
because
no matter what your x-value is.