Question

Bill is twice as old as Adam
Charlie is 3 years younger than Bill
The sum of their three ages is 27
Find the ratio of Adam's age to Charlie's age, giving your answer in the form 1:n

Answer 1

Answer:

$\frac{1}{1.5}$

Step-by-step explanation:

Let B represent Bill age

A be adam age

C be charlie age

We know that

$b = 2a$

We also know that

$c = b - 3$

And we know that

$a + b + c = 27$

Fist let subsitue c for b-3

$a + b + (b - 3) = 27$

$a + 2b - 3 = 27$

$a + 2b = 30$

We know that b=2a so

$a + 2(2a) = 30$

$a + 4a = 30$

$5a = 30$

$a = 6$

Plug that in first equation to solve for b

$b = 2(6)$

$b = 12$

Finally plug that in the final equation to solve for c.

$6 + 12 + c = 27$

$c = 9$

Know we want the ratio of Adam age, a to Charlie age, c.

So we have

$\frac{6}{9} = \frac{2}{3} = \frac{1}{1.5}$