solve the following word problem

Question

Quick Cleaners offers the following specials:  five shirts and two pairs of pants for $12.50 or ten shirts and three pairs of pants for $22.00.  Write and solve a system of equations to find the charge for each shirt and pair of pants.

Answer 1

Let s = shirt and p = pants:

5s + 2p = 12.5

10s + 3p = 22

 

I suggest we use elimination to solve this. By multiplying the first equation by -2, that will give us -10s to cancel the 10s in the other equation:

-10s - 4p = -25

10s + 3p = 22

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

-p = -3

p = 3

 

Now that we have p, we can solve for s and check our answer:

5s + 2 * 3 = 12.5

5s + 6 = 12.6

5s = 6.5

s = 1.3

 

10 * 1.3 + 3 * 3 = 22

13 + 9 = 22

22 = 22

 

So pants cost $3.00 and shirts $1.30.