Turn into an equation and solve

Question

A is 10 years olde than B. Two years ago, A was six times B's age. How old is B now?

Answer 1

2 equations

A = B+10 (a is ten years older than b)

A-2=6(B-2)  (2 yrs ago a was 6 times b)

 

Plug first equation into second equation for A

A-2=(B+10)-2 = B+8

Thus 

B+8 = 6(B-2) 

Foil and solve for B

B+8 = 6B-12 WHICH MEANS 

20 = 5B

SO 

B = 4

From first equation

A=B+10 = 14

 

thats our answer. 

Doing a check we see

A-2 =12 and 6(B-2) = 6*2 = 12

 

Best - david

Answer 2

A = 10 + B

A-2 = 6*(B-2)

 

Substituting A from equation 1 into equation 2:

(10+B) - 2 = 6(B-2)

 

10 + B - 2 = 6B - 12

 

8 + B = 6B - 12

 

20 = 5B

 

B = 4 years old now