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# math

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

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1. 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

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2. 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.

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3. 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 .

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