You need to rent the car for 3 weeks. Ace Car Rental agency charges $0.29 per mile plus a $10 weekly fee. Elite Rental agency charges $.0.35 per mile with no fee.
5a. Write and solve an equation to find the number of miles for which both agencies will charge the same.
5b. Which agency offers the better deal if you plan to drive at least 1000 miles during the three weeks. Explain and show your work!

a. 0.29x + 10 = 0.35x

b. Ace Car Rental agency offers the better deal.

Step-by-step explanation:

a. Let the number of miles = x

For company Ace Car Rental agency,

per mile charges = $0.29

charges for x miles = $0.29x

Since company charges a weekly fee = $10

Therefore, the total charges of the company = $0.29x + 10

For company Elite Rental agency,

Total charges for x miles = $0.35x

If both the company charge the same

Then, the equation will be,

0.29x + 10 = 0.35x

10 = 0.35x - 0.29x

10 = 0.06x

x = 166.67 miles

At 166.67 miles both agencies will charge the same.

b. If you plan to drive at least 1000 miles during the three weeks.

Hence, x = 1000 miles

Charges of Ace Car Rental agency :

Rental per mile(distance to be covered) + weekly charge (number of weeks)

= $0.29(1000) + $10(3)

= $290 + $30

= $330

Charges of Elite Rental agency

= $0.35 (1000)

= $350

For 1000 miles during 3 weeks Ace Car Rental agency offers the better deal.

step-by-step explanation:

the true statements are:

r = set of real numbers

n = set of natural numbers, 1,2,

w = n u{0} = {0,1,}