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Ron wants to deliver a package to his friend. He is considering two courier services to do the job.

The first courier service is charging a flat fee of $15 plus $3 per pound of the package's weight.

y=3x+15


The second courier service is charging a flat fee of $25 plus $2 per pound of the package's weight.

y=2x+25


The costs of the two courier services are shown in the graph.





What must the package weigh for the costs of the two courier services to be the same?

(1 point)
Responses

12
12

14
14

8
8

10

1 answer

To find the weight at which the costs of the two courier services are the same, we need to set the equations for both services equal to each other and solve for \(x\) (the weight of the package).

The equations are:

  1. For the first courier service: \(y = 3x + 15\)
  2. For the second courier service: \(y = 2x + 25\)

Setting the equations equal to each other:

\[ 3x + 15 = 2x + 25 \]

Now, subtract \(2x\) from both sides:

\[ 3x - 2x + 15 = 25 \]

This simplifies to:

\[ x + 15 = 25 \]

Next, subtract 15 from both sides:

\[ x = 25 - 15 \]

Thus,

\[ x = 10 \]

Therefore, the package must weigh 10 pounds for the costs of the two courier services to be the same. The correct response is 10.