I don't get this!!! I have tried so many times for about an HOUR and I need help!!!

Question

Three girls were comparing their scores. Joan has 2 times as many as Alyssa. Alyssa has 6 more than Mary. Together the three girls have a total score of 70. What is each girl's score?

Answer 1

Hi Emma,

 

Let Alyssa's score be x (this is what I did. You can assign a different girl, too). Then, Joan's score is 2x and Mary's score is x-6. Is this where you had problems? The rest is easy.

 

x + 2x + (x-6) = 70

4x - 6 = 70

4x = 76

x = 19

 

Can you find the other girls' score?

Answer 2

Let j = Joan's score

Let a = Alyssa's score

Let m = Mary's score

 

Joan's score is 2 times Alyssa's

j = 2a

 

Alyssa has 6 more than Mary

a = m + 6

 

Together they have a score of 70

j + a + m = 70

 

Using substitution replace j with2a

2a + a + m = 70

 

Since a=m+6

then m = a-6

 

Using substitution again, replace m 

with a-6

 

2a+a+a-6 = 70

combine like terms

4a - 6 = 70

add 6 to both sides

4a = 76

divide both sides by 4

a = 19

 

We now have Alyssa's score.

j = 2a = 2(19) = 38

m = a-6 = 19-6 = 13

 

Alyssa got 19

Joan got 38

Mary got 13

 

Answer 3

Hi Emma, let x represent Mary's score. Then Alyssa's score is: x + 6, and Joan's score is: 2 * (x + 6). Total score is 70.

 

Equation:

 

x + (x + 6) + 2 * (x + 6) = 70

 

x + x + 6 + 2x + 12 = 70

 

Combine terms:

 

4x = 52

 

x = 13

 

Therefore:

 

Mary's score is 13.

 

Alyssa's score is 13 + 6, or 19.

 

Joan's score is 2 * 19, or 38

 

Questions?