En En packed all 732 cookies into a mixture of large and small boxes. He filled each large box with 30 cookies and each small box with 22 cookies. All the boxes are filled with no cookies left over. What is the least number of boxes used by En En? Ans: ___

1. Set up the equation for the total number of cookies.

Let the number of large boxes be $x$ and the number of small boxes be $y$.
$30x + 22y = 732$
Dividing by 2 to simplify:
$15x + 11y = 366$

2. Find the maximum possible number of large boxes to minimize the total number of boxes.

To use the least number of boxes, we must use as many large boxes as possible.
The maximum possible value for $x$ is $366 \div 15 = 24.4$, so we test integer values of $x$ starting from $24$ downwards to see which gives a whole number for $y$.
If $x = 24$, $11y = 366 - 15(24) = 6$ (not divisible by 11)
If $x = 23$, $11y = 366 - 15(23) = 21$ (not divisible by 11)
If $x = 22$, $11y = 366 - 15(22) = 36$ (not divisible by 11)
If $x = 21$, $11y = 366 - 15(21) = 51$ (not divisible by 11)
If $x = 20$, $11y = 366 - 15(20) = 66$, so $y = 6$.

3. Calculate the least total number of boxes.

Total number of boxes = $x + y = 20 + 6 = 26$.