Algebra Word Problem

Question

Bobby is two years less than twice as old as Fanny.  In four years, Fanny will be 3/4 as old as Bobby will be then.  How old  are they now?

Answer 1

b = 2f - 2

f + 4 = (3/4)(b + 4)

 

Substitute!

 

f + 4 = (3/4)(2f - 2 + 4)

f + 4 = (3/4)(2f + 2)

(4/4)f + 16/4 = (6/4)f + 6/4

(1/2)f = 5/2

f = (5/2)2

f = 5

 

b = 2(5) - 2

b = 8

 

Bobby is 8 and Fanny is 5.

 

Answer 2

B = 2F - 2

 

 

3/4(B+4) = F+4  ---> 3/4 B + 3 = F + 4

                                 3/4 B - 1 = F

 

B = 2( (3/4) B - 1) - 2

 

B = (3/2)B - 2 - 2

B = (3/2)B - 4

 

0 = (1/2)B - 4

 

4 = (1/2)B

B = 8

 

Bobby is 8

Fanny is 3/4(8) - 1 = 6-1 = 5

 

In 4 years, Bobby will be 12 and Fanny will be 9 and 3/4 of 12 is 9