A local delivery service charges a flat fee of 12 dollars plus 1.50 dollars per mile to de… — SAT

A local delivery service charges a flat fee of $12$ dollars plus $1.50$ dollars per mile to deliver a package. If a customer wants to spend no more than $30$ dollars for a package delivery, what is the maximum number of miles the delivery service can travel?

Answer: 12 miles

Answer

The maximum number of miles the delivery service can travel is 12.

The total delivery cost is the sum of the flat fee (

12

dollars) and the rate per mile (

1.50

dollars multiplied by

m

miles), which is represented by

1.50m + 12

. Since the total cost cannot exceed

30

dollars, the inequality is

1.50m + 12 \leq 30

. Subtracting

12

from both sides gives

1.50m \leq 18

. Dividing both sides by

1.50

yields

m \leq 12

. Thus, the maximum distance the delivery service can travel is

12

miles.

Step-by-Step Solution

Set up the inequality representing the delivery cost constraint.

1.50m + 12 \leq 30

The total cost of the delivery is the flat fee of

12

dollars plus

1.50

dollars per mile,

m

, which must be less than or equal to the budget of

30

dollars.

Subtract 12 from both sides of the inequality.

1.50m \leq 18

To isolate the variable term, subtract the constant flat fee from both sides of the inequality.

Divide both sides of the inequality by 1.50.

m \leq 12

Dividing by the per-mile rate calculates the maximum distance constraint on the variable

m

Key Concept

Setting up and solving a one-variable linear inequality to determine a maximum boundary value in context.

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