Isha has written down five numbers. The mean of these numbers is 13.2, the median is 12 and the mode is 7. The largest number is three times the smallest number. Find the five numbers in ascending order.

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

Mean $=13.2$

Total of the five numbers:
$13.2 \times 5 = 66$

2. Use the median, mode, and largest-smallest relationship to find the numbers.

Since the numbers are in ascending order and the median is $12$, the middle number is $12$.

Since the mode is $7$, the number $7$ must appear twice before $12$:
$7,\ 7,\ 12,\ d,\ e$

The smallest number is $7$, so the largest number is
$3 \times 7 = 21$

So
$7+7+12+d+21=66$
$47+d=66$
$d=19$

Hence the five numbers are
$7,\ 7,\ 12,\ 19,\ 21$