Question

37 For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92. The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76. Write a system of equations to represent the costs of a juice box, j, and a bottle of water, w. Kara said that the juice boxes might have cost 52 cents each and that the bottles of water might have cost 33 cents each. Use your system of equations to justify that Kara's prices are not possible. Solve your system of equations to determine the actual cost, in dollars, of each juice box and each bottle of water.

Answer 1

Explanation:

Let j represent the cost of a juice box.

Let w represent the cost of a bottle of water.

One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92.. This means that

18j + 32w = 19.92 - - - - - - - - - - - - 1

The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76. This means that

14j + 26w = 15.76- - - - - - - - - - - - 2

Multiplying equation 1 by 14 and equation 2 by 18, it becomes

252j + 448w = 278.88

252j + 468w = 283.68

Subtracting, it becomes

- 20j = - 4.8

j = - 4.8/- 20 = 0.24

Substituting j = 0.24 into equation 1, it becomes

18 × 0.24 + 32w = 19.92

4.32 + 32w = 19.92

32w = 19.92 - 4.32 = 15.6

w = 15.6/32 = 0.4875

Kara's prices are incorrect.

the cost of a juice box is $0.24

the cost of a bottle of water is $0.4875