Short sleeve shirts $6 Long sleeve shirts are $24 If the store sells all 30 shirts, it can make a total of $594.How many of each type of shirt is needed?

Question

 I need to write an equation that helps me solve for the number of Long Sleeve and Short Sleeve shirts sold. I know the answer is 23 long sleeve and 7 short sleeve but am struggling with the equation. I believe it is

Answer 1

x=# of short

30-x=#of long

6x+24(30-x)=594

6x+720-24x=594

-18x+720=594

-18x=594-720

-18x=-126

18x=126

x=126/18

x=7

30-7=23

Answer 2

These types of problems always contain one piece of information on how many items and one on the price. thiese let you set up the two equations.

 

So L= the number oflong sleeve and s = short sleeve shirts.

 

So we have a total of 30 shirts...........so S + L = 30

The price equation would be ...............6S + 24L = 594

 

Multiply the top equation by -6 to get

 

-6S - 6L = -180

6S  + 24L = 594

 

Add them to get

18L = 414

L = 23

 

Plug it back in to either equation to get S = 7.

 

Hope this helped.