Question

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 Boxes of water and spent $15.76

Answer 1

Cost of each juice boxes is $ 0.68 and cost of each water bottle is $ 0.24

Solution:

Let "j" be the cost of each juice box

Let "w" be the cost of each bottles of water

One teacher purchased 18 juice boxes and 32 bottles of water and spent $19.92

Therefore, we frame a equation as:

18 x cost of each juice box + 32 x cost of each bottles of water = 19.92

`18 * j + 32 * w = 19.92`

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

The other teacher Purchased 14 Juice Boxes and 26 Boxes of water and spent $15.76

Therefore, we frame a equation as:

14 x cost of each juice box + 26 x cost of each bottles of water = 15.76

`14 * j + 26 * w = 15.76`

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

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 7

126j + 224w = 139.44 -------- eqn 3

Multiply eqn 2 by 9

126j + 234w = 141.84 ---------- eqn 4

Subtract eqn 3 from eqn 4

126j + 234w = 141.84

126j + 224w = 139.44

( - ) --------------------

10w = 2.4

Divide both sides by 10

w = 0.24

Substitute w = 0.24 in eqn 1

18j + 32(0.24) = 19.92

18j + 7.68 = 19.92

18j = 12.24

Divide both sides by 18

j = 0.68

Thus cost of each juice boxes is $ 0.68 and cost of each water bottle is $ 0.24