word problem

Question

On Saturday night, the manager of a shoe store evaluates the receipts of the previous week's sales. Two hundred fifty pairs of two different styles of running shoes were sold. One style sold for $75.50 and the other sold for $89.95. The receipts totaled $29,604. The cash register that was supposed to record the number of each type of shoe sold malfunctioned. Can you recover the information? If so, how many shoes of each type were sold? (Use either addition or substitution to solve)

Answer 1

Hi! Here we need two equations using the information we are given in order to "play detective!" Think "two equations, two unknown." We know we need to make a system and solve it.

We know there are 250 pairs of shoes and that some are style "x" and some are style "y."

We can define our x and y as follows

x = number of shoes at $75.50

y = number of shoes at $89.95

and "total" number of shoes is 250, we know we need to add.

This information will give us our first equation.

x + y = 250

This deals with number of shoes, now we need to look at cost of shoes.

Think total cost of x shoes plus total cost of y shoes = grand total cost

75.50x + 89.95y = 29,604

Using substitution (one of our choices to solve) we can find what y is "in terms of x". This just means let's use the first equation and get y all by itself.

x + y = 250

-x           -x

---------------------

y = 250 - x

Now we can put "25 - x" in for "y"

75.50x + 89.95 ( 250 - x ) = 29,604

Next "distribute" that 89.95 to each term, and we get

75.50x + 22487.50 - 89.95x = 29,604

Combine "like terms" on the left side of the equation sign

- 14.45x + 22487.50 = 29,604

              - 22487.50    - 22487.50

-----------------------------------------------

-14.45x            =         7116.5

Next, we divide to get x by itself

-14.45x/-14.45  = 7116.5/-14.45

x = -492.49

Hmmmmmmm, that would mean we would have a "negative" number of shoes, and a "half a pair" to boot! No pun intended....At this point, you need to check the numbers in the original question and check your math. I'm pretty sure my math is correct, so make sure you copied the problem down right! At any rate, I hope this explanation helped! Best, Joanne