Question

Maggie makes some fruit punch. She mixes 2 1/2 quarts of grape juice with 1 1/2 quarts of orange juice. One quart of grape juice costs $1 less than one quart of orange juice. She finds that the total cost of making fruit punch is $12.50. Calculate the cost of each quart of grape juice and each quart of orange juice.

Answer 1

The cost of each quart of orange juice=$3.75

The cost of each quart of grape juice=$2.75

Explanation:

The expression for the total cost of making fruit punch is as follows;

Total cost of making fruit punch=total cost of making grape juice+total cost of making orange juice

where;

Total cost of making fruit punch=$12.50

Total cost of making grape juice=Cost per unit of grape juice×total quantity of grape juice

Total cost making grape juice=(2 1/2)×g=2.5 g

Total cost of making orange juice=Cost per unit of orange juice×total quantity of orange juice

Total cost of making orange juice=(1 1/2)×o=1.5 o

replacing;

12.50=2.5 g+1.5 o...equation 1

But price per unit of grape juice is one dollars less that the price per unit of orange juice;

Price per unit of orange juice=o

Price per unit of grape juice=(o-1), g=o-1

replace the value of g=o-1 in equation 1;

12.50=2.5 g+1.5 o...equation 1

12.50=2.5(o-1)+1.5 o

12.50=2.5 o-2.5+1.5 o

2.5 o+1.5 o=12.50+2.50

4 o=15

o=15/4=3.75

g=o-1=3.75-1=2.75

The cost of each quart of orange juice=o=$3.75

The cost of each quart of grape juice=g=$2.75