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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


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Respuesta :

JeanaShupp

Answer: (A)  [tex]y = 0.55x + 5.5[/tex]

Step-by-step explanation:

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

Equation for total charge: [tex]y=mx+n[/tex] , 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 :-

[tex]10m+n=11----------(1)\\\\ 5m+n=8.25----------(2)[/tex]

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

[tex]5m=2.75[/tex]

Divide both sides by 5 , we get

[tex]m=0.55[/tex]

Put m= 0.55 in (2), we get

[tex]5(0.55)+n=8.25\\\\ 2.75+n=8.25\\\\ n=8.25-2.75=5.5[/tex]

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 :

[tex]y = 0.55x + 5.5[/tex]

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