Question

Beth is two years older than Julio. Gerald is twice as old as Beth. Debra is twice as old as Gerald. The sum of their ages is 38. how old is Beth?

Answer 1

Beth is five years old.

Step-by-step:

Beth + Julio + Gerald + Debra = 38

B + (Beth - 2) + (2 x Beth) + (2 x Gerald) = 38

Since we know that Gerald is twice as old as Beth and Debra is twice as old as Gerald. That makes Debra four times older than Beth.

Beth + (Beth - 2) + (2 x Beth) + (4 x Beth) = 38

B + (B -2) + (2B) + (4B) = 38

Simplfy the like terms.

8B - 2 = 38

Add 2 on both sides.

8B = 38 + 2

8B = 40

Divide both sides by 8 to isolate the variable.

8/8 B = 40/8

B = 5