Question

Suzy went to a department store and brought 3 pairs of shoes. The first pair of shoes were not too expensive, but the second pair was twice as much as the first pair. The third pair of shoes were $5 more than the first pair. She paid with a $100 bill and got $3 in change. How much did each pair of shoes cost?

Answer 1

Cost of first pair shoe = a = $23

Cost of second pair shoe = b = $46

Cost of third pair shoe = c = $28

Explanation:

Let

Cost of first pair shoe = a

Cost of second pair shoe = b

Cost of third pair shoe = c

The first pair of shoes were not too expensive, but the second pair was twice as much as the first pair.

b = 2a......... Equation 1

The third pair of shoes were $5 more than the first pair.

c = a + 5...... Equation 2

She paid with a $100 bill and got $3 in change.

a + b + c = $100 - $3

a + b + c = 97........... Equation 3

Substitute 2a for b and a + 5 for c in Equation 3

a + 2a + a + 5 = 97

4a = 97 - 5

4a = 92

a = 92/4

a =$23

The cost of the first pair of shoe = $23

b = 2a......... Equation 1

b = 2($23)

b = $46

The cost of the second pair of shoe = $46

c = a + 5...... Equation 2

c = $23 +$5

c = $28

The cost of the third pair of shoe = $28