Question

UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound.
How many pounds, p, will it take for UPS and FedEx to cost the same? What is the cost? Write and solve an equation to show your work.

Answer 1

Answer:

1. 20 pounds

2. $11

Step-by-step explanation:

To set this up, you have to use a system of equations. It would look like this, where $p$ is pounds and $t$ is total cost:

UPS: $t=7+0.20p$

FedEx: $t=5+0.30p$

In order to solve a system of equations you must either a.) graph it, or b.) set them equal to each other.

If you graph it, the answer is where the two lines intersect.

If you set them equal to each other, solve it.

I will set them equal to each other in this:

$7+0.20p=5+0.30p$

The first step in a problem like this, where there's the same variable on both sides, is to subtract the smaller variable from both sides. In this case, it is  $0.20x$. That would turn the equation into:

$7=5+0.10p$

After that, you must solve it like a regular two-step equation.

Start by subtracting 5 from both sides:

$2=0.10p$

Now, you must divide both sides by $0.10$.

$\frac{2}{0.10}=\frac{0.10p}{0.10}$

That would give us:

$20=p$

This means that in order for the prices to be the same, the package must be 20 pounds.

Now in order to find the total cost, you must plug 20 into one of the equations. It doesn't matter which, since they both equal the same. I will plug it into the FedEx equation:

$t=5+0.30(20)$

Now you can just use a calculator and solve that or do it by hand. Multiply 0.30 by 20, to get 6, then add 5, which equals 11.

You should get: $t=11$.

This means that the total cost, when the costs are the same for both FedEx and UPS, is $11.