Ivanna is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.

Company A charges 114 and allows unlimited mileage.
Company B has an initial fee of 65 and charges an additional 0.70 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m

To determine the mileage at which Company A will charge less than Company B, we need to set up an inequality and solve for m.

The cost for Company A is a flat rate of $114, irrespective of the number of miles driven.

For Company B, the cost consists of an initial fee of $65 plus an additional $0.70 for each mile driven. Therefore, the cost for Company B can be expressed as 0.70m + 65, where m represents the number of miles driven.

To find the mileage at which Company A charges less than Company B, we set up the inequality:

114 < 0.70m + 65

Now, we can solve this inequality for m:

114 - 65 < 0.70m
49 < 0.70m
70 < m

Therefore, Company A will charge less than Company B when the number of miles driven, m, is greater than 70.

Melissa is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.

Company A charges an initial fee of $50 and an additional 80 cents for every mile driven.
Company B charges an initial fee of 65$ and an additional 60
cents for every mile driven.

Lena is choosing between two exercise routines.

In Routine #1, she does only running, burning 10.5 calories per minute.
In Routine #2, she burns 23 calories walking. She then runs at a rate that burns 4.75 calories per minute.
For what amounts of time spent running will Routine #1 burn more calories than Routine #2?
Use for the number of minutes spent running, and solve your inequality for .

let the mileage be m

65 + .7m < 114 + 0m
.7m < 49
m < 70

so for m> 70 miles, company A is cheaper

check:
if m = 50
company A charges $114
company B charges 65 + .7(50) = 100

if m = 71
company A charges $114
company B charges 65+.7(71) = $114.70 . which is more

btw, if m = 70
A charges $114
B charges 65 + 70(.7) = 114 , the same