SOLUTION: This is a word step equation. I'll type it down. Renting in-line skates and safety equipment costs 3.50 per hr. Renting ONLY safety equipment costs 1.50 an hour. You can buy used i

Algebra ->  Inequalities -> SOLUTION: This is a word step equation. I'll type it down. Renting in-line skates and safety equipment costs 3.50 per hr. Renting ONLY safety equipment costs 1.50 an hour. You can buy used i      Log On


   

Question 1097858: This is a word step equation. I'll type it down. Renting in-line skates and safety equipment costs 3.50 per hr. Renting ONLY safety equipment costs 1.50 an hour. You can buy used in-line skates from your friend for $40 OR you can rent some. Either way, you must rent safety equipment. How many hour smust you skate for the cost of renting skates be more than not renting skates? (Hint: This inequality involves the variable on both sides. I started and this is where I got. 3.50h 40. From there I was thinking of many solutions. Please help me solve
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if you rent both then the cost is 3.50 * x, where x is the number of hours skate.

if you buy the skates, then the cost is 40 + 1.50 * x.

the 40 is up front one time fixed cost and the 2.50 per hour is the cost of renting the safety equipment.

you want to know when the cost of renting skates is more than the cost of buying skates.

your equation would be 3.50 * x > 40 + 1.50 * x

subtract 1.50 * x from both sides of this equation and you get 2.00 * x > 40

divide both sides of this equation (actually an inequality) and you get x > 20.

you would have to skate more than 20 hours for the cost of renting the skates to be more than the cost of buying the skates.

test this out with x < 20 and x = 20 and x > 20

i used x = 18, 20, and 22.

cost of renting skates versus cost of buying skates table is shown below: 



hours             buy skates                 rent skates         cheaper


18                40 + 18 * 1.50 = 67        18 * 3.50 = 73      rent


20                40 + 20 * 1.50 = 70        20 * 3.50 = 70      both the same


22                40 + 22 * 1.50 = 73        22 * 3.50 = 77      buy


the cutoff is at 20 when the cost of buying and renting is the same.
any hours over that and the cost of buying the skates is less than renting both.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

This is a word step equation. I'll type it down. Renting in-line skates and safety equipment costs 3.50 per hr. Renting ONLY safety equipment costs 1.50 an hour. You can buy used in-line skates from your friend for $40 OR you can rent some. Either way, you must rent safety equipment. How many hour smust you skate for the cost of renting skates be more than not renting skates? (Hint: This inequality involves the variable on both sides. I started and this is where I got. 3.50h 40. From there I was thinking of many solutions. Please help me solve
See your OTHER post: Inequalities/1097861: