Using slove if equations

Question

A sporting goods store sells right handed and left handed baseball gloves. In one month 12 gloves were sold for a total of revenue of $561. Right handed gloves cost $45 and left handed gloves cost $52. How many of each type of glove today s how many of each type of glove did they sell. 

Answer 1

Let R = number of right handed gloves, L = number of left handed gloves

 

Then

 

R*($45) + L($52) = $561

R + L = 12

 

This is a system of 2 linear equations in 2 unknowns R and L:

 

45R + 52L = 561

R + L = 12

 

From the bottom equation, get R = 12 - L and substitute this into the top equation:

 

45(12-L) + 52L = 561

540 - 45L + 52L = 561

7L = 21

L = 21/7 = 3

 

Now substitute L = 3 into R = 12 - L and get 

 

R = 12 - L = 12 - 3 = 9

 

So in 12 months the store sold 9 right handed gloves and 3 left handed gloves.