Math algebra math

Question

Deborah is 7 years younger than Bob. In 6 years Bob will be twice as old as Deborah. How old is bob now

Answer 1

The first sentence is equivalent to writing (B == Bob's age and D == Deborah's age):

D = B - 7

The second sentence is equivalent to writing:

(B + 6) / (D + 6) = 2

Using substitution we can solve for Bob's age:

(B + 6) / (B - 7 + 6) = 2

(B + 6) / (B - 1) = 2

Now multiply both sides by (B - 1)

B + 6 = 2 * (B - 1)

B + 6 = 2 * B - 2

Now subtract B from both sides

6 = B - 2

Lastly add 2 to both sides:

8 = B

Bob is 8 years old.