Respuesta :
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,
[tex]x=2+2y\ldots\ldots.1[/tex]And also, we were told that Margaret and Nathan spent a total of $128 at the state fair.
Mathematically,
[tex]x+y=\text{ \$128}\ldots\ldots\ldots2[/tex]Let us substitute 'x'= 2+2y into equation 2 and solve for y.
[tex]\begin{gathered} x+y=128 \\ 2+2y+y=128 \\ 2y+y=128-2 \\ 3y=126 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3y}{3}=\frac{126}{3} \\ y=42 \end{gathered}[/tex]Therefore, the amount of money spent by Nathan will be,
[tex]\begin{gathered} x=2+2y \\ x=2+2(42)=2+84=86 \\ \therefore x=86 \end{gathered}[/tex]Hence, Nathan spent $86 at the fair.
