A DVD costs twice as much as a music CD. Jack buys 2 DVDs and 2 CD's and spends $45. Determine how much one CD costs, in dollars.

Question

This question is on solving word problems using linear equations.

Answer 1

Give DVD and CD a variable

DVD = d

CD = c

 

Set up 2 equalities to express what you know

d = 2c

2d + 2c = 45        reduces down to d + c = 22.50

 

Now you have a system of 2 equations and 2 unknowns, substitute the first equation into the 2nd equation so that you are working with 1 variable.

 

2c + c = 22.50

3c = 22.50

 

c = 7.50

 

a CD costs $7.50, 2x7.50 = $15 or the price of a DVD

check yourself by plugging in c = 7.5 and d = 15

2 (15) + 2(7.5) = 45

30 + 15 = 45

Answer 2

Here's what we know:

D = 2C (A DVD has the same cost as 2 CDs)

2D + 2C = 45

 

Since we have a value for D, we can put that into our equation:

2(2C) + 2C = 45

4C + 2C = 45

6C = 45

C = 7.50

 

So a CD costs $7.50