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?

Since they both rent the vehicles at the same price, "x" for jet skis and "y" for kayaks", we can create equations for each store and a system of equations for these, as shown below:

Watersports:

12*x + 9*y = 780

Fun Rentals:

7*x + 11*y = 570

System:

[tex]\left \{ {{12*x + 9*y=780} \atop {7*x + 11*y=570}} \right.[/tex]

We can isolate "x" on the first equation:

[tex]x = \frac{780 - 9*y}{12}[/tex]

And use it on the second:

[tex]7*[\frac{780 - 9*y}{12}] + 11*y = 570\\5460 -63*y = 6840 - 132*y\\132*y - 63*y = 6840 - 5460\\69*y = 1380\\y = 20\\[/tex]

We can now use this value to find "x":

[tex]x = \frac{780 - 9*20}{12} = 50[/tex]

Therefore Jet Skis cost $50 for the rental and Kayaks cost $20.