Question

A recipe for sparkling grape juice calls for 1.5 quarts of sparkling water and .75 quart of grape juice. A. How much sparkling water would you need to mix with 9 quarts of grape juice? B. How much grape juice would you need to mix with 3.75 quarts of sparkling water?

Answer 1

Answer: We need to mix 18 quarts of sparkling water with 9 quarts of grape juice.

We need to mix 1.875 quarts of grape juice with 3.75 quarts of sparkling water.

Step-by-step explanation:

Given: A recipe for sparkling grape juice calls for 1.5 quarts of sparkling water and .75 quart of grape juice.

Since, for recipe of sparkling grape juice , they should be used in same proportion.

Let x be the amount of sparkling water need to mix with 9 quarts of grape juice, then

$\frac{x}{9}=\frac{1.5}{0.75}\\\Rightarrow\ x=\frac{1.5\times9}{0.75}\\\Rightarrow\ x=18$

We need to mix 18 quarts of sparkling water with 9 quarts of grape juice.

Let y be the amount of grape juice need to mix with 3.75 quarts of sparkling water, then

$\frac{3.75}{y}=\frac{1.5}{0.75}\\\Rightarrow\ y=\frac{3.75\times0.75}{1.5}\\\Rightarrow\ y=1.875$

We need to mix 1.875 quarts of grape juice with 3.75 quarts of sparkling water.

Answer 2

Answer:you would need 18 quarts of sparkling water to mix with 9 quarts of grape juice

Step-by-step explanation:

1 1/2 ---------> 3/4

x --------------> 9

We clear the value of x:

x = ((9) / (3/4)) * (1 1/2)

Rewriting we have:

x = ((9) * (4/3)) * (1 1/2)

x = (36/3) * (1 1/2)

x = (12) * (1 1/2)

x = (12) * (3/2)

x = 18

Answer:

you would need 18 quarts of sparkling water to mix with 9 quarts of grape juice