Two snow resorts offer private lessons to their customers. Big Time Ski Mountain charges $5 per hour plus $50 insurance. Powder Hills charges $10 per hour plus $30 insurance. For what number of hours is the cost of lessons the same for each resort?
Big Time Mountain : Cost = 5x + 50
Powder Hill : Cost = 10x + 30
when is
10x + 30 = 5x + 50 ? solve for x
To find the number of hours for which the cost of lessons is the same for both resorts, we need to set up an equation and solve for the unknown variable.
Let's represent the number of hours as 'h.'
For Big Time Ski Mountain, the cost of lessons can be calculated using the equation:
Cost = 5h + 50
For Powder Hills, the cost of lessons can be calculated using the equation:
Cost = 10h + 30
To find the number of hours where the costs are equal, we set the two equations equal to each other:
5h + 50 = 10h + 30
Now let's solve for 'h.'
Subtract 5h from both sides of the equation:
50 = 5h + 30
Subtract 30 from both sides of the equation:
20 = 5h
Divide both sides by 5:
4 = h
Therefore, the cost of lessons is the same for both resorts after 4 hours of lessons.
To find the number of hours for which the cost of lessons is the same for each resort, we need to set up an equation and solve for the unknown variable.
Let's denote the number of hours of the lesson as 'h'.
For Big Time Ski Mountain, the cost of the lesson is calculated as:
Cost_BigTime = 5h + 50
For Powder Hills, the cost of the lesson is calculated as:
Cost_PowderHills = 10h + 30
We want to find the number of hours for which the cost of lessons is the same, so we can set up the following equation:
5h + 50 = 10h + 30
Now, let's solve for 'h'.
Move all the terms containing 'h' to one side of the equation and the constant terms to the other:
5h - 10h = 30 - 50
Simplifying the equation gives us:
-5h = -20
To isolate 'h', we divide both sides of the equation by -5:
h = (-20) / (-5)
h = 4
Therefore, the cost of lessons is the same for both resorts when the number of hours is 4.