Question

At an after-season sale on winter clothes, I found a bunch of really cute hats and scarves. I decided to buy two hats and two scarves for myself to have for next year. I spent $72. When I told my friends about the sale, they asked me to go back and get something for them. I ended up spending $46 on one hat and two scarves. What was the price of a single hat and a single scarf?Write two integers separated by comma, no spaces, no dollar sign

Answer 1

One hat costs $26 and one scarf costs $10

Step-by-step explanation

Let the price of one hat be h.

Let the price of one scarf be s.

Two hats and two scarves cost $72. This implies that:

`2h+2s=72`

One hat and two scarves cost $46. This implies that:

`h+2s=46`

From the second equation, make h the subject of the formula:

`h=46-2s`

Substitute that into the first equation and solve for s:

`\begin{gathered} 2(46-2s)+2s=72 \\ 92-4s+2s=72 \\ \Rightarrow92-72=4s-2s \\ 2s=20 \\ \Rightarrow s=(20)/(2) \\ s=\$10 \end{gathered}`

Substitute the value of s into the equation for h and solve for h:

`\begin{gathered} h=46-2(10) \\ h=46-20 \\ h=\$26 \end{gathered}`

Hence, one hat costs $26 and one scarf costs $10.