Question

Two beach rental companies compared their sales from last weekend. Both companies rent out jet skis and kayaks, and they charge the same prices. Will's Watersports made a total of $780 from renting 12 jet skis and 9 kayaks. Family Fun Rentals made a total of $570 from renting 7 jet skis and 11 kayaks. What is the cost of each type of rental?

Answer 1

To rent a jet ski you need to pay $50 and to rent a kayak you need to pay $20

Explanation:

Since both shops charge the same amount for each kind of vehicle, we will assign variables to the their cost. The cost of a jet ski will be "x" and the cost of the kayak will be "y". Therefore we can create a system of equations as shown below:

Will's shop:

12*x + 9*y = 780

Fun Rentals:

7*x + 11*y = 570

`\left \{ {{12x+ 9y=780} \atop {7x + 11y =570}} \right.\\`

We can isolate "x" on the second equation, we have:

`x = (570 - 11y)/(7)`

Applying this value on the first equation:

`12[(570 - 11y)/(7)] + 9y = 780\\(6840 - 132y)/(7) + 9y = 780\\(6840 - 132y + 63y)/(7) = 780\\ 6840 - 132y + 63y = 5460\\6840 - 69y = 5460\\69y = 1380\\y = 20`

Applying the value of "y" we found on the "x" equation above, we have:
`x = (570 - 11*20)/(7)\\x = 50\\`

Therefore to rent a jet ski you need to pay $50 and to rent a kayak you need to pay $20