## Subject 4.

Let $x$ be the age of the youngest daughter, $m$ be the age of the mother, and $t$ be the age of the father.

The ages of the other two daughters will be $x+2$ and $x+4$.

From the relationships: \quad $t + m + x + (x + 2) + (x + 4) = 88$

$x + (x + 2) + (x + 4) = m - 10$ and

$t = m + x$

we obtain that $x = 5$, which means:

the daughters are 5, 7, and 9 years old

the mother is 31 years old

the father is 36 years old.

![](https://cdn.mathpix.com/cropped/2024_06_07_f98a9d6c106196fc3d80g-2.jpg?height=212&width=310&top_left_y=68&top_left_x=496)

## MATHEMATICS OLYMPIAD  LOCAL STAGE  FEBRUARY 9, 2013

## GRADE 5
## Subject 4.

The sum of the father's, mother's, and the three daughters' ages is 88 years. The sum of the ages of the three daughters is 10 years less than the mother's age. The father's age is equal to the mother's age plus the age of the youngest daughter. One of the daughters is two years younger than another and two years older than the third. How old is each?

## Note: All subjects are mandatory  Time allowed: 3 hours