Question

The sum of positive integers b and h is 34. If their difference is 8, what is the value of bh ?

Select one:
A. 25
B. 56
C. 75
D. 273

Answer 1

b+h=34 and b-h=8

So b=8+h

8+h+h=34

2h=26

h=13

b=21

bh=21*13=273

D is your answer

Answer 2

D

given the 2 expressions, construct 2 equations

b + h = 34 → (1)

b - h = 8 → (2) with b > h

add (1) and (2) term by term to eliminate h

2b = 42 ⇒ b = 21

substitute b = 21 in (1) and solve for h

21 + h = 34 ⇒ h = 34 - 21 = 13

hence bh = 21 × 13 = 273 → D