Question

A recipe for sparkling grape juice calls for

1/2
quarts of sparkling water and 3/4
quarts 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 15/4
quarts of sparkling water?

c. How much sparkling water would you need to make 100 quarts of punch?

d. How much grape juice would you need to make 100 quarts of punch?

Answer 1

Answer:. A.) 6 quarts

B.) 45/8 quarts

C. 40 quarts sparkling water and 60 quarts of grape juice.

Once you get the basic ratio which is the amount of sparkling water is 2/3 the amount of grape juice, you can use that to set up as n equation for the next two questions.

Explanation:

15/4 = 2x/3

Multiply both sides by the reciprocal:

3/2(15/4 = 3/2(2x/3)

45/8 = x

That is 5 5/8 quarts when simplified.

15/4 is 3 3/4 quarts

2 parts sparkling water to 3 parts grape juice is another useful ratio. Using that, 2x + 3x= 100 we can calculate

5x = 100

x 20. 2(20)=40 and 3(20)= 60

Answer 2

A) 3/4 is equal to 0.75. 1/2 is equal to 0.5. You need to find out how many parts of the grape juice you have. So you take your 9 quarts and divide it by 0.75. That equals 12. So for the 9 quarts you need, you will add 12 parts of the 3/4. Now you need to add 12 1/2s as well. So 1/2 (or 0.5) multiplied by 12 is 6. So your answer would be 6 quarts