**The Mango Problem**

By: Taylor, Madi, and Marsella

The Mango Problem

One night the King couldn't sleep, so he went down into the Royal kitchen, where he found a bowl full of mangoes. Being hungry, he took 1/6 of the mangoes. Later that same night, the Queen was hungry and couldn't sleep. She, too, found the mangoes and took 1/5 of what the King had left. Still later, the first Prince awoke, went to the kitchen, and ate 1/4 of the remaining mangoes. Even later, his brother, the second Prince, ate 1/3 of what was then left. Finally, the third Prince ate 1/2 of what was left, leaving only three mangoes for the servants. How many mangoes were originally in the bowl?

Solution Method

How We Solved It

Our solution method was the 'work backwards' strategy. We used this strategy because at the end of the problem, the fractional amounts are smaller and easier to work up to the bigger fractions. You could also use;

- guess and check

- an equation

- drawing

1.

If the bowl ended up with a remainder of 3 mangoes and the Third Prince took 1/2 of the pile, before the Third Prince took his share, there were 6 meaning the Third Prince took 3 mangoes. We know this because 3 is half of 6.

2.

There were 6 mangoes in the bowl and the Second Prince took 1/3 of what was left (6 were left), we multiplied 3 by the denominator of the fraction 1/3 (which is 3) to get 9 which was how many there were before the Second Prince took his share.

How We Solved It (continued)

3.

There were now 9 mangoes in the bowl. The First Prince took 1/4 of what was then left in the bowl (9 were left). To figure out how many were in the bowl before that, we multiplied the ending amount of mangoes (which was 3) by the denominator of 1/4 (which is 4) and got 12 which were how many mangoes in the bowl before the First Prince took his share.

4.

There are now 12 mangoes in the bowl to be shared and the Queen took 1/5 of what was left. If the First Prince had left 9, than we multiplied 3×5 and got 15, then we take the fractional amount of mangoes that the Queen took (which is 1/5) and multiplied the denominator of her fraction by the ending number of mangoes and got 15, which was the amount of mangoes left in the bowl before the Queen took her share.

How We Solved It (continued)

5.

The very last step we took was the amount left in the bowl before the King took his share. To get this, we took the last amount of mangoes in the bowl (3) and multiplied that by the denominator of the fractional amount the King wanted to take (which was 1/6) and we got 18.

**Final Answer**

Our final answer is...

This is the only possible answer for this method because if you use guess and check or an equation you will still get the answer 18 from the clues in the problem.

Mathemtical Practices

The mathematical practices we used were...

- Make sense of problems and perservere in solving them (1).

- Look for and make use of structure (7).

The first mathematical practice helped us when we made sense of the problem by reading the problem over more then once. We then decided what method we would use to solve the problem. We never gave up when it was hard.

Practice #1

Practice #7

The seventh mathematical practice helped us when we used the structure by using the clues it gave us in the problem. We then took those clues and created a reasonable answer.

The Pattern we Noticed

The pattern we noticed was that by multiplying the ending number of mangoes (which was 3) by the denominator of each fractional amount of mangoes eaten, you would get the next number. By doing 3×6 (which is the last amount of mangoes times the Kings fractional amount) you get 18 which was our solution.

Thank you for coming to watch our presentation! We hope you enjoyed ;)