Question

Ethan is deciding between two parking garages. Garage A charges an initial fee of $7
to park plus $4 per hour. Garage B charges an initial fee of $10 to park plus $3 per
hour. Let A represent the amount Garage A would charge if Ethan parks for t hours,
and let B represent the amount Garage B would charge if Ethan parks for t hours.
Write an equation for each situation, in terms of t, and determine the interval of
hours parked, t, for which Garage A is cheaper than Garage B.
A=
B =
Garage A is cheaper than Garage B when t

Answer 1

Answer:

A= 4t + 7

B= 3t+10

Garage A is cheaper than Garage B when t < 3 hours.

Step-by-step explanation:

Garage A charges $7 just to enter the garage even for t=0 hours, and will charge and additional $4 per hour parked. Therefore the amount Garage A would charge for t hours of parking is: A= 4t + 7

Garage B charges 10 just to enter the garage even for t=0 hours, and will charge and additional $3 per hour parked. Therefore the amount Garage B would charge for t hours of parking is: B= 3t+10

To find the number of hours, t, that would make the parking garages cost the same, set the two equations equal to each other and solve for t:

4t + 7 = 3t + 10

-3          -3

t + 7 =  + 10

- 7          -7   t = 3

Since both equation values are equal when t=3, we know that the two garages would charge an equal amount when parking for 3 hours.

Since Garage A has less expensive initial fee ($7 vs. $10), Garage A will continue to be less expensive until it "catches up" to Garage B at t=3 hours

When t is less than 3 hours, Garage A is cheaper.

Answer 2

The equations representing the situation and when garage A is cheaper than B is required.

The required equations are

$A=7+4t$

$B=10+3t$

Garage A is cheaper when the time to be parked is less than 3 hours.

System of linear equations

The required equations are

$A=7+4t$

$B=10+3t$

where $t$ = number of hours.

The point where the price is same will be

$7+4t=10+3t\\\Rightarrow t=\dfrac{10-7}{4-3}\\\Rightarrow t=3$

when $t=2$

$A=7+4\times 2=15$

$B=10+3\times 2=16$

when $t<3$ then garage A is cheaper.

when $t=4$

$A=7+4\times 4=23$

$B=10+3\times 4=22$

when $t>3$ then garage B is cheaper.

Learn more about system of linear equations:

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