Expert: Josh - 5/3/2011

Question
Jenny is y^2 yrs old and her daughter allyson is y yrs old.
if jenny lives to the age of 13y ,allyson will be y^2 yrs old.How old is Allyson now.

Answer
Hi Athena,

To solve this problem, let us deal with each piece of information one by one.

Our objective is to find the age of Allyson now (last part of the second sentence).
Remember, the current age of Allyson is denoted by "y" (last part of the first sentence).

The relationship between the current age and future age of a person is described by:
Future Age = Current Age + Number of Elapsed Years  ......[Equation 1]

At some point in the future (say T years from now), Jenny's age will be "13y" when her daughter's age will be y^2. Using Equation 1, we get

For Jenny:  y^2+T = 13*y [Equation 2]
For Allyson: y+T = y^2   [Equation 3]

[The key is adding a constant offset in years to their current age to get their future age]

Making T as the subject from [3], we obtain T = y^2 - y. To solve for "y", we may eliminate "T" from [2] by substituting T=y^2-y into Equation [2]. This gives:

y^2 +(y^2-y) = 13y.
2*y^2-14y = 0.

After factorization, we get
2y (y-7) = 0.

Both y=0 and y=7 are possible solutions. However, we reject y=0 as the actual answer since it makes no sense for both mother and daughter to have age zero (this, by definition, means they don't exist). The final answer is therefore y=7; this is the current age of Allyson. Mom's age is y^2=49.

You can verify that T=y^2-y=42. i.e., 42 years later, mom's age will be 13*y = 91 when Allyson will be the same age as her mother now (y*y = y+T = 49).