Gladys wrote down four numbers. The mean of these numbers is 13, the median is 12 and the mode is 10. Find the four numbers.

1. Use the mean to find the total of the four numbers.

Mean $=13$ for $4$ numbers.

$\text{Total}=13\times 4=52$

2. Use the median and mode to determine the four numbers.

Arrange the numbers in ascending order as

$a,\ b,\ c,\ d$

For four numbers, the median is the mean of the two middle numbers.

$\frac{b+c}{2}=12$

$b+c=24$

The mode is $10$, so $10$ must be repeated. Since the numbers are in ascending order, the first two numbers are

$10,\ 10$

Then

$\frac{10+c}{2}=12$

$10+c=24$

$c=14$

Using the total:

$10+10+14+d=52$

$d=18$