Mrs Smith has some sweets to distribute to her students. If she gives each student 3 sweets, she will be **left** with 24 **extra** sweets. If she gives each student 5 sweets, she will be **short** of 42 sweets.

How many sweets does Mrs Smith have?

*This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:*

*Homeschooling for gifted kids*
*Preparation for GEP (Gifted Education Programme) screening and selection tests*
*Preparation for Math Olympiad*
*Puzzles for kids interested in math but find school work too easy.*

**Solution**

This is quite a tricky problem for Grade 2-4 students. The main problem is that the number of sweets, as well as the number of students is unknown! Many students will not know how to even start solving such questions.

We can reason as follows:

From 3 sweets each to 5 sweets each is an **increase of 5-3=2 sweets each.**

From having 24 **extra** sweets to being **short** of 42 sweets is a difference of **24+42=66 sweets**.

Hence, to cause the above difference, there must be a total of 66/2=33 students!

Then, we can conclude:

33 students x 3 sweets each = 99 sweets

99+24=123 sweets altogether.

**Answer: 123 sweets**

We can also check our answer using another method:

33 students x 5 sweets each = 165 sweets

165-42=123 sweets.

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