Question

John paid $222 for four hours of skiing and two hours boating. He paid $213 for two hours skiing and three hours boating. What is the cost pero hour of each activity?

Answer 1

Skiing costs $30 per hour and Boating costs $51 per hour.

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":

`4x+2y=222`

"He paid $213 for two hours skiing and three hours boating":

`2x+3y=213`

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.

`2x+3y=213\\2x=213-3y\\x=(213-3y)/(2)\\Equation 1: 4x+2y=222\\Substituting :\\4((213-3y)/(2))+2y=222\\2(213-3y)+2y=222\\426-6y+2y=222\\426-222=6y-2y\\204=4y\\y=(204)/(4)=51`

Hence, y = 51

Now, substituting this y value into the 1st equation and solving for x will give us the value of x.

`First Equation: 4x+2y=222\\4x+2(51)=222\\4x+102=222\\4x=222-102\\4x=120\\x=(120)/(4)=30`

Hence, skiing costs $30 per hour and boating costs $51 per hour.