Question

Problem SolvingNicholas is 32 years older than Martina. 9 years ago the sum of their ages was 56. How old is each now?

Answer 1

Nicholas is 53 years old now

Martina is 21 years old now

Step-by-step explanation:

Here, we want to get the current ages of Nicholas and Martina

Let Nicholas' age be n while Martina's age be m

Nicholas is 32 years older

Mathematically:

`n\text{ = m + 32}`

9 years ago, the sum of their ages is 56

Mathematically:

`\begin{gathered} (m-9)\text{ + \lparen n-9\rparen = 56} \\ m+n\text{ - 18 = 56} \\ m\text{ + n = 18 + 56} \\ m\text{ + n = 74} \end{gathered}`

Now, we have two equations that we can solve simultaneously:

`\begin{gathered} n\text{ = m + 32} \\ m\text{ + n = 74} \end{gathered}`

Substitute equation i into ii:

`\begin{gathered} m\text{ + 32 + m = 74} \\ 2m\text{ + 32 = 74} \\ 2m\text{ = 74-32} \\ 2m\text{ = 42} \\ m\text{ = }(42)/(2) \\ m\text{ = 21} \end{gathered}`

Recall:

`\begin{gathered} n\text{ = m + 32} \\ n\text{ = 21 + 32} \\ n\text{ = 53} \end{gathered}`