Question

The total cost of a jacket and a tie was $70.71. If the price of the jacket was $5.09 less than the tie, what was the price of the jacket? Express your answer as a simplified fraction or a decimal rounded to two places.

Answer 1

Let:

x = cost of the jacket

y = Cost of the tie

The total cost of a jacket and a tie was $70.71 so:

`x+y=70.71`

the price of the jacket was $5.09 less than the tie, so:

`\begin{gathered} x=y-5.09 \\ so\colon \\ y=x+5.09 \end{gathered}`

Replace y into the original equation:

`\begin{gathered} x+(x+5.09)=70.71 \\ 2x+5.09=70.71 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 2x=70.71-5.09 \\ 2x=65.62 \\ x=(65.62)/(2) \\ x=32.81 \end{gathered}`

Answer:

$32.81