Question

Sally bought some candy bars for $1.25 each and some sodas for $1.49 each. If she bought a total of 38 items and spent $50.38 how many of each item did she buy?

Answer 1

• 26 candy bars
• 12 sodas

Explanation:

Let s represent the number of sodas Sally bought. (We chose sodas for the variable because those were the more expensive item.) Then the number of candy bars is (38-s), and we can write an equation for the total cost:

1.25×(38 -s) + 1.49×s = 50.38

0.24s + 47.50 = 50.38 . . . . simplify

0.24s = 2.88 . . . . . . . . . . . . subtract 47.50

2.88/0.24 = s = 12 . . . . number of sodas

38-s = 38-12 = 26 . . . . . number of candy bars

Sally bought 26 candy bars and 12 sodas.

Answer 2

26 candy bars and 12 sodas

Explanation:

This problem can be solved by a simple system of equations

I am going to call x the number of candy bars that Sally bought and y the number of sodas that Sally bought.

The fact that she bought 38 itens means the x + y = 38.

She spent $50.38. The value she spent is the sum of the number of candy bars multplied by the value of the candy bar and the number of sodas multiplied by value of a soda. So 1.25x + 1.49y = 50.38

So we have to solve the following system:

1)x + y = 38

2)1.25x + 1.49y = 50.38

From 1), we have that x = 38 - y. I am going to replace it in 2)

1.25(38-y) + 1.49y = 50.38

-1.25y + 1.49y = 50.38 - 47.5

0.24y = 2.88

y = 12.

Sally bought 12 sodas.

In 1: x = 38-y = 38-12 = 26

Sally bourght 26 candy bars