Would greatly appreciate all answers Thanks 1 Solve the prob

Would greatly appreciate all answers! Thanks.

1. Solve the problem by writing and solving a suitable system of equations.
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $126 for 3 days and 300 miles, while Mary was charged $235 for 5 days and 600 miles. What does Best Rental charge per day and per mile?

A) $17 per day and 25 cents per mile

B) $16 per day and 26 cents per mile

C) $18 per day and 26 cents per mile

D) $25 per day and 17 cents per mile

2. Write a cost function for the problem. Assume that the relationship is linear.
A moving firm charges a flat fee of $30 plus $25 per hour. Let C(x) be the cost in dollars of using the moving firm for x hours.

A) C(x) = 25x - 30

B) C(x) = 30x - 25

C) C(x) = 25x + 30

D) C(x) = 30x + 25

3. Solve the problem.
Midtown Delivery Service delivers packages which cost $1.80 per package to deliver. The fixed cost to run the delivery truck is $105 per day. If the company charges $8.80 per package, how many packages must be delivered daily to reach the equilibrium point?

A) 9 packages

B) 15 packages

C) 10 packages

D) 58 packages

4. Determine whether the given ordered set of numbers is a solution of the system of equations.

(6, -2)
x + y = -8
x - y = -4

Yes or no?

5. Determine whether the given ordered set of numbers is a solution of the system of equations.

(-3, 2)
x + y = -1
x - y = -5

No or Yes?

6. Solve the problem.

The bank\'s temperature display shows that it is 34° Celsius. What is the temperature in Fahrenheit?

A) 118.8°

B) 93.2°

C) 1.1°

D) 36.7°

Solution

1) x be the cost per mile

y be the cost per day

Barney:

He was charged $126 for 3 days and 300 miles

cost for 3 days = 3y , cost for 300 miles = 300x

==> Total cost = 300x + 3y = 126

==> 300x + 3y = 126 ---------- (1)

Mary:

She was charged $235 for 5 days and 600 miles

cost for 5 days = 5y , cost for600 miles = 600x

==> Total cost = 600x + 5y = 235

==> 600x + 5y = 235 ---------- (2)

Solving (1) and (2)

2*(1) - (2) ==>

600x + 6y - ( 600x + 5y) = 252 - 235

==> y = 17

substitute y = 17 in (1)

==> 300x + 3(17) = 126

==> 300x = 126 - 51

==> 300x = 75

==> x = 75/300

==> x = 0.25

Hence $17 per day and 25 cents per mile. (Option A)

2) Flat fee = $30

fee for 1 hour = $25

==> fee for x hours = 25x

Hence total fee C(x) = fee for x hours + Flat fee

==> total fee C(x) = 25x + 30 (Option C)