Question

Kevin delivers groceries to people’s homes. He charges a fixed rate per mile and also a fixed delivery fee. When Kevin makes a 10-mile trip to deliver groceries, he charges $11. When he makes a 5-mile trip to deliver groceries, he charges $8.25. Which equation could be used to determine the amount of money (y), in dollars, Kevin will charge when he makes a trip of x miles to deliver groceries?

(A) y = 0.55x + 5.5


(B) y = 0.8x + 3


(C) y = x + 1


(D) y = 2x – 1.75


Group of answer choices

Answer 1

Answer: (A)
`y = 0.55x + 5.5`

Explanation:

Let m be the fixed rate charged by Kevin and n be the fixed delivery fee.

Equation for total charge:
`y=mx+n` , where y is the amount of money ( in dollars) Kevin will charge when he makes a trip of x miles to deliver groceries.

Then, the system of equation for the given descriptions will be :-

`10m+n=11----------(1)\\\\ 5m+n=8.25----------(2)`

Subtract equation (2) from equation (1), we get

`5m=2.75`

Divide both sides by 5 , we get

`m=0.55`

Put m= 0.55 in (2), we get

`5(0.55)+n=8.25\\\\ 2.75+n=8.25\\\\ n=8.25-2.75=5.5`

Now, the equation could be used to determine the amount of money (y), in dollars, Kevin will charge when he makes a trip of x miles to deliver groceries will be :

`y = 0.55x + 5.5`