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