Question

Kira wanted to stock up on drinks for an upcoming party. First, she spent $53 on 14 cases of

juice and 11 cases of soda, which is all the store had in stock. A few days later, she returned
to the store and purchased an additional 14 cases of juice and 8 cases of soda, spending
total of $50. What is the price of each drink?

Answer 1

Juice is $3.00

Soda is $1

Explanation:

Let j = the cost of 1 juice

Let s = the cost of 1 soda

14j + 11s = 53

14j + 8s = 50 ⇒multiply through by -1 ⇒-14j - 8s = -50 Add this to the first equation.

14j + 11s = 53

-14j - 8s = -50

3s = 3 Divide both sides by 3

`(3s)/(3)` =
`(3)/(3)`

s = 1

It costs $1.00 for every soda.

Replace s with 1 in either of the original equations.

14j + 11s = 53

14j + 11(1) = 53

14j + 11 = 53 Subtract 11 from both sides

14j + 11 - 11 = 53 - 11

14j = 42 Divide both sides by 14

`(14j)/(14)` =
`(42)/(14)`

j = 3

It coes $3.00 for every juice.

Check:

14j + 11s = 53

14(3) + 11(1) = 53

42 + 11 = 53

53=53 Checks

14j + 8s = 50

14(3) + 8(1) = 50

42 + 8 = 50

50 = 50 Checks