Can you help me solve this?

Question

Marcello is an artist who makes oil paintings and charcoal sketches. He sells each oil painting for $500 and each sketch for $300. If Marcello wants to create 56 works in total, how many pieces of artwork must he sell in order to make exactly $20,000?

Answer 1

p : number of oil paintings

s : number of sketches

 

(equation 1): s + p = 56 (total number of works)

 

(equation 2): 500*p (total cost of paintings) + 300*s (total cost of sketches) = 20,000 (total cost of works)

 

 

Substitution method:

 

you rewrite equation 1: s = 56 - p 

 

you substitute the s in equation 2 to solve for p:

 

500*p + 300*(56-p) = 20,000

(500-300)*p + 300*56 = 20,000

200*p = 20,000 - 300*56

200*p = 3200

p = 3200/200 = 16

 

s = 56 - 16 = 40