How do you solve this using the substitution method?

Question

A DVD costs twice as much as a CD. Jack buys 2 DVDs and 1 DC and spends $25. Determine the cost of each item.

Answer 1

Hi Abigail,

Happy to help!

First, you're going to want to write two equations in terms of d for DVDs and c for CDs. Don't worry about having both d and c in the same equation at first. That is expected.

If 1 DVD costs twice as much as a CD, we can write that as:

1d = 2c

The other piece of information we have is the cost of the purchase. Jack buys 2 DVDs and 1 CD, spending $25:

2d + 1c = $25

Now let's solve one equation for one of the variables. I chose to solve the first equation for d because that's already done for us, but you could solve the second equation or you can solve for c and this will still work.

d = 2c

Next you'll substitute (plug-in) the expression you have for d (or whatever you solved for) into the second equation, so where you have d in 2d + 1c = $25, you'll plug in 2c:

2(2c)+ 1c = $25

Now you can solve for c:

4c + 1c = $25

5c = $25

c = $5

Now that you solved for c, you can plug that value into either equation with d and solve for d. I chose the simpler one:

1d = 2c

1d = 2($5)

d = $10

And that's your answer! c = $5, d = $10

You can plug those numbers into either equation to double check your work! Jack buys 2 DVDs at $10 (=$20) and 1 CD at $5 and spends $25! Looks good to me!

And that's the substitution method in a nutshell!

I hope this helps!

-Carly

Answer 2

D = 2C

2D + C = 25

2(2C) + C = 25

Can you solve for C and answer?