# Bob is 8 years younger than charlie. Doug is 2 years older than charlie. The sum of Charlie and Dougs ages is 4 times bobs age. How do you find the age of all boys. math problem?

Jan 12, 2016

Charlie is 17 , Bob is 9 and Doug is 19.

#### Explanation:

This type of problem is referred to as mathematical modelling.

This means converting a word problem into an equation which can then be solved.

Start by allocating a variable (letter symbol) to one of the boys.

In this case say Charlie is x (years old)

From this we can write that Doug = x + 2 ( as he is 2 years older than Charlie)

and Bob = x - 8 (as he is 8 years younger)

Charlie and Doug's added together (sum) =4 times Bob's age. Now using our symbols from above (Algebra).We obtain the following :

x +(x + 2 ) = 4 (x - 8 ) which can be written as :

2x + 2 = 4x _ 32 .To solve this equation collect numbers to the left hand side ( of the = sign) and variables to the other.

2+ 32 = 4x - 2x gives 34 = 2x and x = 17

Finally then: Charlie = x = 17 : Bob = x - 8 = 17 - 8 = 9

and Doug = x + 2 = 17 + 2 = 19

check: Charlie + Doug = 17 + 19 = 36 and 4times Bob's age =4 $\times$ 9 =36.