Question

Haley needs to rent a moving van for the day. Company A charges $75 plus $0.25 per mile. Company B charges $50 plus $0.75 per mile. For how many miles is company B less expensive than company A?

Answer 1

Haley needs to rent. Till 49.99 miles, Company B will be less expensive than company A.

Solution:

Given that

Haley needs to rent a moving van for the day.

Charges of company A are $75 plus $0.25 per miles

That means $75 is fixed price and $0.25 depends on travelling miles.

Charges of company B are $50 plus $0.75 per miles That means $50 is fixed price and $0.75 depends on travelling miles.

Need to calculate for how many miles is company B less expensive than company A.

Let’s assume for "x" miles company B is less expensive than company A.

Lets create expression for charges of each company for "x" miles.

For company A,

Fixed charges = $75

For 1 mile charges = $0.25

So for x miles = 0.25x

Total charges of company A for x miles
`=\mathrm{C}_{\mathrm{A}}=75+0.25 x`

For company B,

Fixed charges = $50

For 1 mile charges = $0.75

So for x miles = 0.75x

Total charges of company B for x miles
`=\mathrm{C}_{\mathrm{B}}=50+0.75 x`

we need to find value of x such that

`\mathrm{C}_{\mathrm{B}}<\mathrm{C}_{\mathrm{A}}`

=> 50 + 0.75x < 75 + 0.25x

=> 0.75x - 0.25x < 75 – 50

=> 0.5x < 25

=> x < 50

So till 49.99 miles , Company B will be less expensive than company A.

At 50 miles charges of both the company will be same.