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.
This question can be solved using the “units” method, and “working backwards”.
At the end, Bob had 5 times as many marbles as Aaron.
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.