Answer:
Skiing costs $30 per hour and Boating costs $51 per hour.
Step-by-step explanation:
Let cost per hour of skiing be x and cost per hour of boating be y. Let's dissect the problem into 2 simultaneous equations.
"John paid $222 for four hours of skiing and two hours boating":
[tex]4x+2y=222[/tex]
"He paid $213 for two hours skiing and three hours boating":
[tex]2x+3y=213[/tex]
Now, if we solve for x in the 2nd equation and plug it in the 1st equation, we will have the value for y. Work shown below.
[tex]2x+3y=213\\2x=213-3y\\x=\frac{213-3y}{2}\\Equation 1: 4x+2y=222\\Substituting :\\4(\frac{213-3y}{2})+2y=222\\2(213-3y)+2y=222\\426-6y+2y=222\\426-222=6y-2y\\204=4y\\y=\frac{204}{4}=51[/tex]
Hence, y = 51
Now, substituting this y value into the 1st equation and solving for x will give us the value of x.
[tex]First Equation: 4x+2y=222\\4x+2(51)=222\\4x+102=222\\4x=222-102\\4x=120\\x=\frac{120}{4}=30[/tex]
Hence, skiing costs $30 per hour and boating costs $51 per hour.
