### Brain Teasers

# How Young?

Mr. and Mrs. Silver have three daughters.

When the youngest was born, you could multiply the middle child's age by three to get the oldest sister's age.

Nine years ago, you could add the middle child's age to the youngest child's age to get the oldest child's age.

What is the youngest that the oldest child can be now?

When the youngest was born, you could multiply the middle child's age by three to get the oldest sister's age.

Nine years ago, you could add the middle child's age to the youngest child's age to get the oldest child's age.

What is the youngest that the oldest child can be now?

### Hint

You can create two equations, where the three variables are:- the age of the middle child when the youngest child was born

- the age of the oldest child when the youngest child was born

- the age of the youngest child 9 years ago.

### Answer

The oldest child must presently be at least 14 years old.Ages at youngest child's birth (youngest to oldest):

0, y, z

Ages 9 years ago (or x years after the youngest child was born; youngest to oldest):

0+x, y+x, z+x

There are two restrictions:

(1) At the youngest child's birth we know that 3y=z

(2) Nine years ago, the oldest child must be the sum of her two youngest sibling's ages, so x+x+y=x+z

Simplifying the two equations, we get:

z=3y

x=2y

From there, we input the lowest possible value of y, and calculate the oldest child's present age:

z+x+9

(3y)+(2y)+9

3+2+9 = 14

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