KAREN SPENT $131 ON SHIRTS. FANCY SHIRTS COST $28 AND NORMAL SHIRTS COST $15. SHE BOUGHT 7. HOW MANY OF EACH SHIRT DID SHE BUY

Question

 KAREN SPENT $131 ON SHIRTS. FANCY SHIRTS COST $28 AND NORMAL SHIRTS COST $15. SHE BOUGHT 7. HOW MANY OF EACH SHIRT DID SHE BUY

Answer 1

a) Define the variables: x is the number of normal shirts, y is the number of fancy shirts, a is the price of normal shirt, b is the price of fancy shirt

 

b) Set up the equations representing the relationships

equation 1: a = 15

equation 2: b = 28

equation 3: x + y = 7

equation 4: (a*x) + (b*y) = 131

 

c) Solve the equations

Substitute eq. 1 and 2 into 4 gives

(15*x) + (28*y) = 131

15x + 28y = 131

Divide by 15

(15/15)x + (28/15)y = 131/15

(15/15)x + (15/15)y + (13/15)y = 131/15

x + y + (13/15)y = 131/15

Substitute eq. 3 into above

7 + (13/15)y = 131/15

Multiply by 15

105 + 13y = 131

13y =26

y = 2

Substitute above into eq. 3

x + y = 7

x + 2 = 7

x = 5

Answer: Karen bought x = 5 normal shirts and y = 2 fancy shirts.