Alvin is 8 years younger than Elga. The sum of their ages is 42. What is Elgar’s age?

Answer 1

There are some words we can pick out when reading a word problem that will pretty much always mean the same thing. When writing an equation from a sentence, the word "is" will almost always translate to an equals sign. So "Alvin is" becomes "A =".

We also know that when talking about ages, younger than means less than, so Alvin's age is 8 years less than Elga's age. This means we are subtracting 8 from Elga's age to get Alvin's age. So,

A = E - 8

"The sum of their ages is 42." The sum means the answer to an addition. So,

A + E = 42

We now have a system of two equations. We can solve by substitution or elimination. I think this one is nicely set up for substitution. The first equation is already solved for A, so we just need to plug in "E - 8" where A is in the second equation.

(E - 8) + E = 42

Combine like terms. E + E = 2E

2E - 8 = 42

Move the 8 to the other side by adding it to both sides.

2E = 50

Divide both sides by 2.

E = 25.

So Elga is 25! How old is Alvin? Plug in E = 25 to either equation.

A + 25 = 42

A = 17

Alvin is 17.