Math word problems

Question

You have $60 to spend at the mall. You buy a sweatshirt and a pair of shorts. You are happy that you don't spend all of your money. If the sweatshirt cost $6 more than twice the shorts, how much did you spend on the shorts? Write and solve an inequality to determine the solution.

Answer 1

arkZO is correct, but the question asks you to solve an inequality for the solution.

M = Money for spending
S = Sweatshirt price
SH = Shorts price
CS = Cash spent

We know that you did not spend all your money, so:
1.) CS < M, or CS < 60 and CS > 0  
2.) S = 6 + 2xSH  (sweatshirt is 6 more than twice the shorts price)

We also know the items purchased, 1 sweatshirt and 1 pair of shorts, so:
3.) CS= S + SH  (Cash spent total)

We can now start substituting

CS = 6 + 2xSH + SH  (combine (2) and (3) )
CS = 6 + 3xSH

4.) SH = ( CS - 6 ) / 3

We know that the cash spent (CS) is between $0 and $60
0 < CS < 60

We now have an inequality to solve

0 < 6 + 3xSH < 60

0 < 3x(2 + SH) < 60

divide by 3 on each side

0 < (2 + SH) < 20

-2 < SH < 18

However, we know that the sweatshirt is greater than 0, so

0 < SH < 18

The shorts are less than 18 and greater than 0 

Answer 2

18 or less

60 - 6 equals 54

54 / 3 is 18

 

18 times 2 equals 36

Plus 6 is 42

 

42 + 18 equals 60

 

So the shorts have to be less than $18.