Question

A car service charges customers a flat fee per ride (which is higher during rush hour traffic) plus charges for each minute and each mile. Suppose that, in a certain metropolotian area during rush hour, the flat fee is $3, the cost per minute is $0.20, and the cost per mile is $1.20. Let x be the number of minutes and y the number of miles. At the end of a ride, the driver said that the passenger owed $20.60 and remarked that the number of minutes was five times the number of miles. Find the number of minutes and the number of miles for this trip.

A. Complete the equation that represents the total cost of the ride. ___=20.60

B. Complete the equation that represents the relationship between the number of minutes and number of miles. __=0

C. Find the number of minutes and number of miles for this trip.

Answer 1

x is the number of minutes and y is the number of miles

cost per minute is $0.20 and cost per mile is $1.20

Flat fee is $3

According to question, passenger owed $20.60

So, we can write the equation as

Flat fee + extra cost per minute + extra cost per mile = 20.60

or we can say

(A) $3 + $0.20x + $1.20y = $20.60........................equation for total cost of ride

subtracting 3 on each side, we get 0.20x + 1.2y = 20.6-3.0

so, new equation becomes 0.20x + 1.20y = 17.60..................equation 1

And driver also said that the number of minutes is five times the number of miles

i.e. x = 5y.......................equation 2

subtracting 5y on each side, we get x-5y =5y-5y....................here -5y and 5y will become 0 on right hand side

(B) Equation for relationship between number of minutes and number of miles is x - 5y = 0

Now, using the substitution method, we can place x = 5y in equation1

we get

0.20*(5y) + 1.20y = 17.60

this gives us

1y + 1.2y = 17.60

2.2y= 17.60

dividing both sides by 2.2, we get

(2.2y)/2.2 = 17.60/2.2......................................here (2.2y)/2.2 becomes y because 2.2 and 2.2 divides and gives 1.

y = 8 miles

and using equation 2, we can write x = 5y

putting y = 8

we get

x = 5*8 = 40 minutes

(C) So, 40 minutes and 8 miles for this trip