Question

Margaret and Nathan spent a total of $128 at the state fair last weekend. Nathan spent $2 more than twice the amount that Margaret spent. How much did Nathan spend at the fair?

Answer 1

Let 'y' represent the amount Margaret spent at the state fair.

Let 'x' represent the amount Nathan spent at the state fair.

In the next statement, Nathan spent $2 more than twice the amount that Margaret spent.

Mathematically,

`x=2+2y\ldots\ldots.1`

And also, we were told that Margaret and Nathan spent a total of $128 at the state fair.

Mathematically,

`x+y=\text{ \$128}\ldots\ldots\ldots2`

Let us substitute 'x'= 2+2y into equation 2 and solve for y.

`\begin{gathered} x+y=128 \\ 2+2y+y=128 \\ 2y+y=128-2 \\ 3y=126 \end{gathered}`

Divide both sides by 3

`\begin{gathered} (3y)/(3)=(126)/(3) \\ y=42 \end{gathered}`

Therefore, the amount of money spent by Nathan will be,

`\begin{gathered} x=2+2y \\ x=2+2(42)=2+84=86 \\ \therefore x=86 \end{gathered}`

Hence, Nathan spent $86 at the fair.