Question

Word Problem Three girls downloaded a total of 43 songs on their iPods. Jazmine downloaded triple as many as Inez and since Teresa wanted to have the most, she downloaded one more than Jazmine did. How many songs did each girl download? ​

Answer 1

Inez downloaded 6 songs

Jazmine downloaded 18 songs

Tereza downloaded 19 songs

Explanation:

Let x represent the number of songs Inez downloaded

Inez's downloads = x

Jazmine's downloads = 3*x = 3x

Tereza's downloads = 3x+1

=> x+3x+(3x+1) = 43

=> 4x+3x+1 =43

=> 7x+1 =43

=> 7x = 43-1

=> 7x = 42

=> 7x/7 = 42/7

=> x = 6

:. Inez downloaded 6 songs

Jazmine's downloads =3(x)

=3*6= 18

:. Jazmine downloaded 18 songs

Tereza's downloads = 3x+1

=(3*6)+1

=18+1 = 19

:. Tereza downloaded 19 songs

Answer 2

Jazmine: 18

Inez: 6

Teresa: 19

Explanation:

a + b + c = 43 ⇒ first equation

a = 3b ⇒ second equation

c = a + 1 ⇒ third equation

a = songs that Jazmine downloaded

b = song that Inez downloaded

c = songs that Teresa downloaded

from the secon equation:

b = a/3

take the last equation and third equation into the first equation:

a + (a/3) + (a+1) = 43

2a + a/3 = 43 - 1

6a/3 + a/3 = 42

7a/3 = 42

a = 42*3/7

a = 18

b = a/3

b = 18/3

b = 6

c = a+1

c = 18+1

c = 19

Check:

18 + 6 + 19 = 43