Please help, as soon as possible (Grade 9 Math)

Question

Billie is 4 years older than his sister. Seven years ago Billie was 3 times his sisters age. How old is Billie's sister now?

Answer 1

We have two conditions:  NOW and THEN   Let Billie's age NOW = B  and his sister's age NOW = S

 

Step 1:

 

Create the relationships between Billie and his sister.

 

NOW:  B = S + 4

 

THEN (7 years ago):  B - 7 = 3 (S - 7)      This equation says that when Billie was 7 years younger, his sister was 7 years younger, and Billie was 3 times his sister's age THEN.

 

So we have two relationship equations involving B and S.

 

Step 2:

 

Use the THEN equation to solve for B.  We get

B - 7 = 3S - 21  

B = 3S - 21 + 7

B = 3S - 14

 

Step 3:  

 

This gives us two expressions for B.    Let's compare them:  S + 4 = 3S - 14 

 

 

Solve for S:    

4 + 14 = 3S - S   

18 = 2S

9 = S  This is his sister's age NOW as we defined it at the beginning.

 

Using Step 1, Billie's age NOW is:   B = S + 4 = 9 + 4 = 13 

 

So NOW their ages are 9 and 13.

 

Step 4:

 

Let's check the other condition.  Was Bille 3 times his sister's age THEN?

Billie THEN:  13 - 7 = 6

Sister THEN:  9 - 7 = 2

6 is 3 times 2.  So both conditions are met.

 

Let me know if you have any questions.

 

Ms. Horvath