Question

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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 of making the fruit punch is $12.50. Calculate the cost of each quart of grape juice and each quart of orange juice.

Answer 1

Grape juice(G) is 1$ less than Orange juice (O)
G = O - 1

Orange juice and Grape juice is 12.50 total.
O+G=12.50
or
O+O-1=12.50 since G=O-1

Solve
2O-1=12.50
2O=13.50
o=6.75

The cost is 6.75$ per quart of orange juice

Grape is just 1$ less than that. So 6.75-1 = 5.75. Grape juice costs 5.75 per quart.

We have 2 and 1/2 quarts of grape juice and 1 and 1/2 quarts of orange juice. Or 5/2 and 3/2 to make it easier.

Multiply the amount of quarts with the costs per quart.
5/2*5.75= 14.375

3/2*6.75=10.125

Total costs is
14.375+10.125=$24.5

The answer is it costs about $10.13 for orange and $14.38 for grape.