A commercial drone delivery service charges a flat rate of 15.50 dollars per delivery plus… — SAT

A commercial drone delivery service charges a flat rate of $15.50$ dollars per delivery plus a fuel surcharge of $1.80$ dollars per mile. During a promotional event, the service offers a $20\%$ discount off the fuel surcharge only. If the total cost for a specific delivery during this promotion was $27.02$ dollars, how many miles did the drone travel for this delivery?

Answer: 8 miles

Answer

The correct answer is 8. The promotional fuel surcharge is reduced by

20\%

from the normal

1.80

dollars per mile, resulting in a rate of

1.80 \times (1 - 0.20) = 1.44

dollars per mile. The linear equation modeling the total cost for a delivery of

m

miles during the promotion is

15.50 + 1.44m = 27.02

. Subtracting

15.50

from both sides gives

1.44m = 11.52

. Dividing both sides by

1.44

yields the distance

m = 8

miles.

Step-by-Step Solution

Determine the discounted fuel surcharge per mile.

The discounted surcharge is

1.44

dollars per mile.

20\%

discount is applied to the original

1.80

dollars per mile fuel surcharge:

1.80 \times (1 - 0.20) = 1.44

Set up the linear equation representing the total promotional cost.

15.50 + 1.44m = 27.02

, where

m

represents the number of miles traveled.

The total cost is the sum of the flat rate of

15.50

dollars and the promotional fuel surcharge of

1.44

dollars per mile multiplied by the number of miles.

Subtract the flat rate from both sides of the equation.

1.44m = 11.52

To isolate the term with the variable

m

, subtract the flat rate of

15.50

from the total promotional cost of

27.02

Solve for the distance by division.

m = 8

Divide both sides of the equation by the promotional rate per mile,

1.44

, to find the number of miles.

Key Concept

Formulating and solving a multi-step linear equation in one variable with decimals and percentages to represent a real-world scenario.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic