Can't get off the ground with this word problem

[SargeUSMC]

Sgt Homework Helper here......daughter brought home 4 word problems.....did ok with 3, but I can't get the formula for this one....

Rental "A" charges $40+$5/hr (or fraction)
Rental "B" charges $25+$7.50/hr (or fraction)

After how many hours does it become cheaper to rent from "A"?

 

[Deleted member 4993]

Sgt Homework Helper here......daughter brought home 4 word problems.....did ok with 3, but I can't get the formula for this one....

Rental "A" charges $40+$5/hr (or fraction)
Rental "B" charges $25+$7.50/hr (or fraction)

After how many hours does it become cheaper to rent from "A"?

There are several ways to do this - all of those involve finding the time when these rentals become "equal".

using algebra:

Assume after x hours of rentals - A and B are equal. So<

40 + 5 *x = 25 + 7.5 * x

40-25 = 7.5 x - 5x

2.5 x = 15

x = 6

So after 6 hours of rental, A will become cheaper.

Without using Algebra

Initially B is cheaper by $15

After 1 st hour B is cheaper by $12.5

After 2 hours B is cheaper by $10

After 3 hours B is cheaper by $7.50

After 4 hours B is cheaper by $5

After 5 hours B is cheaper by $2.50

After 5 hours B is cheaper by $0 → From now on A is cheaper...

 

[SargeUSMC]

thank you kindly.