Aaron and Bob had some marbles in a box.

At first, Bob had thrice as many marbles as Aaron.

Aaron sold 5 marbles and Bob bought another 35 marbles.

Then, Bob had 5 times as many marbles as Aaron.

How many marbles were there in the box at first?

*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 question can be solved using the “units” method, and “working backwards”.

At the end, Bob had 5 times as many marbles as Aaron.

We write:

Aaron –> 1u

Bob –> 5u

Next, we work one step backwards (**before** Aaron sold 5 marbles and Bob bought another 35 marbles.)

Aaron –> 1u + 5

Bob —> 5u – 35

Now, we calculate what is 3 times of Aaron (thrice of Aaron’s marbles):

3 times of Aaron –> 3u + 15

We can conclude that:

3u+15 = 5u-35

We may draw the above model, after which we can conclude that:

2u –> 15+35=50

1u —> 25

Hence, Aaron had 1u+5 = 30 marbles at the start.

Bob had 5u-35 = 90 marbles at the start.

In total, there are 30+90= 120 marbles at first.

**Ans: 120**

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