Question

While on a ski vacation, a group can rent pairs of skis and snowboards by the week. They get a reduced rate if they rent 7 pairs of skis for every 3 snowboards rented. The reduced ski rate is $45.50 per pair of skis per week, and the reduced snowboard rate is $110 per snowboard per week. The sales tax on each rental is 16%.

The group has $2,500 available to spend on ski and snowboard rentals. What is the greatest number of pairs of skis and snowboards the group can rent if the ratio of pairs of skis to snowboards is 7:3?

Answer 1

The greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.

Explanation:

Given:

A group can rent pairs of skis and snowboards by the week. They get a reduced rate if they rent 7 pairs of skis for every 3 snowboards rented. The reduced ski rate is $45.50 per pair of skis per week, and the reduced snowboard rate is $110 per snowboard per week.

The sales tax on each rental is 16%.

The group has $2,500 available to spend on ski and snowboard rentals.

If the ratio of pairs of skis to snowboards is 7:3.

Now, to find the greatest number of pairs of skis and snowboards rentals.

So, the rent of 7 pairs of skis =
`7* 45.50=\$318.50.`

And the rent of 3 pairs of snowboards =
`3* 110=\$330.`

So, total rental amount of 7 pairs of skis and 3 pairs of snowboards:

`318.50 + 330 = 648.50.`

Now, to get the rental amount after sales tax:

648.50 + 16% of $648.50.

`=648.50 +(16)/(100)* 648.50.`

`=648.50+103.76`

`=\$752.26.`

The total rental amount after sales tax = $752.26.

As the group has available $2,500.

So, the sets according to the given ratio:

`2500/ 752.26 = 3.32.`

`=3\ sets.`

Thus, there are 3 sets of the ratio 7:3.

So, the rental price according to sets are:

The rent of Skis:

`7* 3 = 21`

`21* 45.50= 955.50`

The rent of snowboards:

`3* 3 = 9`

`9* 110 = 990`

So. the total rental amount of skis and snowboards according to sets are:

`955.50 + 990 = 1,945.50`

Now, the amount of rent after sales tax:

$1945.50 + 16% of $1945.50.

`=1945.50+(16)/(100)* 1945.50`

`=1945.50+311.28=\$2256.78.`

Thus, the total cost = $2256.78.

Now, to get the greatest number of pairs of skis to snowboards that can be rent:

`2,500 - 2,256.78 = 243.22`

The cost of 21 pair of skis and 9 pairs of snowboards is $2256.78 and the group has available only $2500 to spend.

Thus, they can rent only 21 pairs of skis and 9 pairs of snowboards.

Therefore, the greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.