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melamori03 [73]
3 years ago
8

John paid $222 for four hours of skiing and two hours boating. He paid $213 for two hours skiing and three hours boating. What i

s the cost pero hour of each activity?
Mathematics
1 answer:
Inga [223]3 years ago
4 0

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.

<em><u>"John paid $222 for four hours of skiing and two hours boating":</u></em>

4x+2y=222

<em><u>"He paid $213 for two hours skiing and three hours boating":</u></em>

2x+3y=213

<em>Now, if we solve for x in the 2nd equation and plug it in the 1st equation, we will have the value for y</em>. Work shown below.

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

Hence, y = 51

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

First Equation: 4x+2y=222\\4x+2(51)=222\\4x+102=222\\4x=222-102\\4x=120\\x=\frac{120}{4}=30

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

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