Question

one day, he bought 5 pairs of socks for $3.50 each and 4 pairs of shoes for d dollars each. He spent a total of $163.50. Write and solve an equation to find the cost of one pair of shoes

Answer 1

• 5·$3.50 +4d = $163.50
• d = $(163.50 -5·3.50)/4 = $36.50

Explanation:

The total purchase amount is the sum of the products of the cost of an item times the number of that item. For 5 items costing $3.50 each and 4 items costing "d" each, the total purchase amount is ...

5·$3.50 +4·d = $163.50

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This is solved by undoing what is done to the variable. The variable is multiplied by 4 and a quantity added to that product. We undo these operations in reverse order.

First we subtract the added quantity:

4d = $163.50 -5·3.50 = $146.00

Then we undo the multiplication by dividing by the coefficient of d:

4d/4 = $146.0/4

d = $36.50

The cost of one pair of shoes is $36.50.