Question

How much more money did the team raise selling sun hats than tumblers

Answer 1

We are given the following information

Cost of tumblers = $10

Cost of sun hats = $5

Total tumblers and sun hats sold = 30

Total amount raised = $190

Let t represent the number of tumblers and h represents the number of sun hats.

Then we can set up the following two equations

`\begin{gathered} t+h=30\quad eq.1 \\ 10t+5h=190\quad eq.2 \end{gathered}`

Let us solve the above system of equations to find the number of tumblers and sun hats sold.

Separate out one of the variables from eq.1

`t=30-h\quad eq.1`

Now, substitute eq.1 into eq.2 and simplify

`\begin{gathered} 10t+5h=190 \\ 10(30-h)+5h=190 \\ 300-10h+5h=190 \\ 300-5h=190 \\ 300-190=5h \\ 110=5h \\ h=(110)/(5) \\ h=22 \end{gathered}`

So, 22 sun hats were sold.

Now, substitute the value of h into eq.1 to find the value of t.

`\begin{gathered} t=30-h \\ t=30-22 \\ t=8 \end{gathered}`

So, 8 tumblers were sold.

Finally, let us find out how much money did the team make selling tumblers and sun hats.

`\begin{gathered} 22*\$5=\$110 \\ 8*\$10=\$80 \end{gathered}`

The team made $110 selling sun hats and $80 selling tumblers.

$110 - $80 = $30

This means that the team made $30 more money selling sun hats than tumblers.

Therefore, the correct answer is $30