juan is trying to decide which parking garage to use

Question

Bargain garage charges a flat fee of $2 plus $4 per hour. Grey's garage charges a flat fee of $8 plus $2 per hour. For how many hours will the cost of parking in either garage be the same, and what will the cost be?

Answer 1

This is essentially a break-even problem:

 

Let the total cost of Bargain's be:  2 + 4x

Let the total cost of Grey's be:  8 + 2x

 

Set these two equations equal to each other to get:

 

2 + 4x = 8 + 2x

 

Next, we want to have the 'x' on the left-hand side of the equal sign, the number on the right-hand side of the equal sign, so we do the following:

 

subtract 2x from both sides of the equation

subtract 2 from both sides of the equation

 

This gives us:

 

2x = 6

 

Next, to solve for 'x', divide out both sides by 2:

 

x = 3

 

So, the break-even hours is:  3

 

The break-even cost is explained by plugging in '3' in lieu of 'x', for both sides of the equation:

 

2 + 4*3 = 14     [Check]

8 + 2*3 = 14     [Check]

 

So, the time wherein the amount of time makes no difference regarding the cost, is at:  3 hours

 

The total amount of cost associated with the 3 hours is:  $14.00