Question

Write a system of equations to describe the situation below, solve using substitution, and fill

in the blanks.
Lindsey is going to ship some gifts to family members, and she is considering two shipping
companies. The first shipping company charges a fee of $13 to ship a medium box, plus an
additional $2 per pound. A second shipping company charges $10 for the same size of box,
plus an additional $3 per pound. At a certain weight, the two shipping methods will cost the
same amount. What is that weight? How much will it cost?
At a weight of *blank*
pounds, the two shipping methods both cost $ *blank*

Answer 1

For the first shipping company, the cost can be described by the equation y = 2x + 13.

For the second shipping company, the cost can be described by the equation y = 3x + 10.

The weight is 3 pounds and the cost is $19.

Step-by-step explanation:

To describe the situation, we will create two equations.

Let's use x to represent the weight in pounds.

For the first shipping company, the cost can be described by the equation y = 2x + 13.

For the second shipping company, the cost can be described by the equation y = 3x + 10.

To find the weight at which the costs are the same, we can set the two equations equal to each other and solve for x.

2x + 13 = 3x + 10.

Subtracting 2x from both sides gives us 13 = x + 10.

Subtracting 10 from both sides gives us 3 = x, so the weight at which the costs are the same is 3 pounds.

To find the cost at this weight, we can substitute x = 3 into either equation.

If we use y = 2x + 13, we get y = 2(3) + 13 = 19.

So at a weight of 3 pounds, the two shipping methods both cost $19.