System of equation form

Question

Write and solve a system of equations that represents each situation. Elaine bought a total of 15 shirts and pants. She bought 7 more shirts than pants. How many of each did she buy?

Answer 1

Hi Claire--

 

Star's solution is correct, but if you need to use a 'system of equations,' that means 2 equations, with 2 variables:

 

s + p = 15

p + 7 = s

 

Then put both equations in the same order on top of one another:

 

s + p = 15

s - p  =  7

 

Subtract the bottom equation from the top one, noting that "minus negative p" means "positive p."

 

So that leaves you with 2p = 8, so p = 4. Plug that back into the original info and you get 11 shirts to go with your 4 pants.

 

Result is the same, and honestly for thise kind of scenario, Star's way is MUCH easier, but they asked for a system, so there you go! :-)

 

Matt in NY

Answer 2

Hi Claire, 

Step One: Create let statements

Let x=the number of pants 

Let 7+x=the number of shirts 

Step Two: Create and equation

(Number of shirts)+(Number of Pants)=(Total Number of Shirts an Pants)

7+x+x=15 Combine like terms

7+2x=15 Subtract 7 from both sides

2x=8 Divide both sides by 2

x=4

∴She bought 4 pants and 11 shirts. 

Best, 

Star