Nona Is One-Third As Old As Her Mother. Five Years Ago, She Was Only One Fifth Of The Age Of Her Mother. How Old Is Nona Now

Nona is one-third as old as her mother. Five years ago, she was only one fifth of the age of her mother. How old is nona now

 

Answer:

Nona is 10 years old today.

Step-by-step explanation:

Step 1: Assigning variable.

The age of Nonas mother will be expressed in "x". On the other hand, Nonas age will also be expressed as a fraction of x (or a fraction of her mothers age).

Always remember that it will be easier if both Nona and her mother is expressed in both variable.

Step 2: Interpret the first statement "Nona is one-third as old as her mother"

At present: Age of Nona= \frac{1}{3} Age of Nonas mother

Since the age of Nonas mother is expressed in x, then equation one and two will be

Age of Nonas mother=x\\ Age of Nona= \frac{1}{3}x

Step 3: Interpret the second statement "Five years ago, she was only one fifth of the age of her mother"

Five years ago: Age of Nona=\frac{1}{5} Age of Nonas mother

Age of Nonas mother= x -5 (where -5 represent "five years ago")

Since Nonas age is expressed as a fraction of her mothers age, then the equation three and four will be

Age of Nonas mother=x-5\\ Age of Nona=\frac{1}{5} (x-5)

Note: If the situation stated is in the future, then use "+" instead of "-".

Step 4: Get the difference of equation 1 and 2 as well as for equation 3 and 4

The format should be uniform for the two (i.e. older-younger or younger-older). In this problem, I will illustrate the older-younger age difference or Age of Nonas mother - Age of Nona.

  1. Equation 1 and 2: x- \frac{1}{3}x
  2. Equation 3 and 4: (x-5)-\frac{1}{5}(x-5)

Step 5: Equate the two difference and solve for "x".

Note: All throughout the years the only thing that will remain the same is their age difference.

  1. x-\frac{1}{3}x=(x-5)-\frac{1}{5}(x-5)
  2. \frac{2}{3}x=x-5-\frac{1}{5}x+1
  3. \frac{2}{3}x=\frac{4}{5}x-4
  4. \frac{2}{3}x-\frac{4}{5}x=-4
  5. -\frac{2}{15}x=-4
  6. x=30 years old

Nonas mother is 30 years old.

Step 6: Find Nonas present age.

  1. Nonas age at present is 1/3 of her mothers
  2. 1/3 of 30 is 10

Therefore, Nona is 10 years old today.


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