Equations help!

Question

n a recent international sport​ competition, the top three Country ​A, Country​ B, and Country C won a total of 127 medals. Country B won 7 more medals than Country C. Country A won 33 more medals than the total amount won by the other two. How many medals did each of the top three countries​ win?

Answer 1

In a recent international sport​ competition, the top three Country ​A, Country​ B, and Country C won a total of 127 medals. Country B won 7 more medals than Country C. Country A won 33 more medals than the total amount won by the other two. How many medals did each of the top three countries​ win?

(1) A + B + C = 127

(2) B = 7+ C

(3) A = 33+ B + C substitute (2) for B in (3)

A = 33 + (7 + C) + C simplify

(4) A = 40 + 2C

Substitute (2) and (4) for A and B into (1)

(40 + 2C) + (7 + C) + C = 127

simplify

4C + 47 = 127

4C = 80

C = 20

Substitute this into (2) and (4) to find B and A

B = 7 + C = 27

A = 40 + 2C = 80

So, A = 80, B = 27, C = 20