Question

Alvin is 9 years older than Elga. The sum of their ages is 89. What is Elga's age?

Answer 1

Hey there!☺

`Answer:\boxed{40}`

`Explanation:`

Elga's age can be represented as "x". If Elga is x years old, then Alvin's age would be represented as "x+9", since Alvin is 9 years older than Elga.

Their combined age is 89. If you were to write that as an equation in terms of "x", you would have the following equation.

`x+x+9=89`

Since the question is asking for Elga's age, which is x, you're going to be solving the equation for the value of x.

First add like terms:
`x+x+9=89 \rightarrow 2x+9=89`

Subtract both sides by 9 to leave x alone:
`2x+9-9=89-9 \rightarrow 2x=80`

Divide both sides by 2 to find x:
`(2x)/(2) = (80)/(2) \rightarrow x=40`

Since x is equal to 40, Elga is 40 years old, and Alvin would be 49 years old.

You can also check if the answer is correct by adding their ages.

`40+49=89\ \br \checkmark`

Elga is 40 years old.

Hope this helps!

`\text{-TestedHyperr}`

Answer 2

Alvin: 49

Elga: 40

Explanation:

1. The equation is 89 = x + (x-9).
2. Remove the parenthesis and combine the like terms. 89 = 2x - 9
3. Add 9 on both sides. 98 = 2x
4. Divide by 2 on both sides. x = 49
5. 49 is the age of Alvin. (49-9) 40 is the age of Elga.