college algebra word problem study guide

Question

A woman is currently 21 years older than her daughter. Eleven years before the current time, the daughter was two-thirds old as her mother. What is the current age of the mother?

Answer 1

At present:

d represents age of daughter

d + 21 represents age of mother

 

Eleven years ago

d - 11 represents age of daughter

d + 21 - 11 represents age of mother

 

Daughter was 2/3 of mother

 

d - 11 = (2/3)(d + 21 - 11)

d - 11 = (2/3)(d + 10)          multiply both sides by 3

3(d - 11) = 2(d + 10)            distribute

3d - 33 = 2d + 20                 subtract 2d form both side

d - 33 = 20                            add 33 to both sides

d = 53

 

The mother is 74 years old.

 

Check:

53 - 11 = (2/3)(74 - 11)

42 = (2/3)(63)

42 = 42