The number of songs on iTunes Dave owns is 8 less than 2 times the number Erica owns. together they own a total of 100 songs on iTunes. How many songs does Dave own?

Answer 1

Set up the variables:

Let x = # of iTunes Erica owns

2x-8 = # of iTunes Dave owns

Set up the equation:

Erica's iTunes + Dave's iTunes = Total iTunes

x + (2x-8) = 100

Now solve:

Combine like terms

x + (2x-8) = 100

3x - 8 = 100

Add 8 to both sides and simplify

3x - 8 + 8 = 100 + 8

3x=108

Divide both sides by 3 and simplify

3x/3=108/3

x= 36 (This is number Erica owns from defining variables section. Need to find number Dave owns)

2x-8 = # of iTunes Dave owns

2(36) - 8 = 64

Dave owns 64 iTunes.

Answer 2

The key to these problems is to define variables properly. What is it that you don't know? The number of songs Dave owns and the number of songs Erica owns.

D = number of songs Dave owns

E = number of songs Erica owns

D is 8 less than 2E, so

D = 2E - 8

D and E together are 100, so

D + E = 100

subtract D from each side

E = 100 - D

Now, solve by substituting 100 - D for E in the first equation

D = 2(100 - D) - 8

Remove parentheses

D = 200 - 2D - 8

Combine like terms

D = 192 - 2D

Add 2D to each side

3D = 192

Divide each side by 3

D = 64

D = number of songs Dave owns, so Dave owns 64 songs.

Answer 3

Dave owns 8 less than 2 times Erica's collection, so let D = Dave's songs and let E = Erica's songs.

D = (2E - 8)

E + D = 100 because that is the total of their two collections.

E = 100 - D, just rearranging.

Now substitute in the value of E into the first equation and solve for D:

D = 2(100 - D) - 8

D = 200 - 2D - 8

3D = 192

D = 64

So, Dave has 64 songs and Erica has 36 songs as they have 100 songs total.

I hope that helps.