Question

A recipe for sparkling grape juice 1 1/2 quarts of sparkling water and 3/4 of grape juice. How much sparkling water woild you need to mix with 9 quarts of grape juice. How much grape juice would you need to mix with 15/4 quarts of sparkling water?

Answer 1

a)
`x = 18\,qt`, b)
`y = 1\,(7)/(8)\,qt`

Explanation:

a) The amount of sparkling water needed is determined by simple rule of three:

`x = (9\,qt)/((3)/(4)\,qt)* (3)/(2)\,qt`

`x = 12* (3)/(2)\,qt`

`x = 18\,qt`

b) The amount of grape juice needed is found by simple rule of three:

`y = ((15)/(4)\,qt)/((3)/(2)\,qt ) * (3)/(4)\,qt`

`y = (30)/(12)* (3)/(4)\,qt`

`y = (90)/(48)\,qt`

`y = (15)/(8)\,qt`

`y = 1\,(7)/(8)\,qt`

Answer 2

According to the recipe the ratio of sparkling water to grape juice = 1 1/2 : 3/4.

Let us convert 1 1/2 into improper fraction and that is 3/2.

Now, 3/2: 3/4 or 3/2 ÷ 3/4 = 3/2 × 4/3 = 2/1 or 2:1.

Therefore, sparkling water quantity is two times of the quantity of grape juice.

Now, we need to find the number of quarts of sparkling water need to mix in 9 quarts of grape juice.

Since, sparkling water quantity is two times of the quantity of grape juice.

Therefore, we need 2 × 9 = 18 quarts of sparkling water to mix in 9 quarts of grape juice.

And now we need to find the number of quarts of grape juice would we need to mix with 15/4 quarts of sparkling water.

Therefore, we need 1/2 × 15/4 = 15/8 quarts of grape juice to mix with 15/4 quarts of sparkling water.