# Pumpkin Pie Problem

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

## Problem

Peter, the pumpkin eater, wanted to make two pies for a party. His mother, a professional pie maker, had a recipe for him to use. However, she always made $80$ pies at a time. She used:

$10$ dozen eggs

$27$ litres of condensed milk

$480$ tablespoons of sugar

$100$ teaspoons of cinnamon

$140$ cups of pumpkin

Peter looked in the cupboard and found:

$4$ cups of pumpkin

$2$ eggs

$1 \frac{1}{2}$ teaspoons of cinnamon

$\frac{2}{3}$ of a litre of condensed milk

$15$ tablespoons of sugar

Did Peter have enough ingredients to make two pumpkin pies for the party or did he need to buy more?

## Getting Started

How will you find out what you need to make two pumpkin pies?

What would you need for ten pies?

## Student Solutions

It looks like Peter is going to have to go shopping!

A way to think about this problem was to find out what proportion of the original recipe Peter required to make the two pies. You might have divided and then perhaps multiplied, depending on your strategy. Using what you know about fractions could have helped. A number of you sent the answer that Peter was short of some of the ingredients. There were two ways that the problem was solved and fully explained. These mathematicians came up with the following solutions and used their knowledge of decimals.

**Ruth who** lives in Gloustershire, decided that the answer to the *Pumpkin Pie Problem* is, he hasn't got enough ingredients to make two pies. She got the answer by dividing the ingredients by 80 and multipliyingby 2. Both **Helena** from Tattingstone School, and **George** of Rosebank Primary School, Leeds, divided mother's recipe by 40. Why do you think they decided to do this?

Here's **Ruth**'s solution, she did an excellent job of setting out her calculations in a chart.

80 pies take | What he needs | What he has got |
---|---|---|

120 Eggs | 3 eggs | 2 eggs |

27L Milk | 0.675L Milk | 0.66L Milk |

480 tbs. Sugar | 12 tbs. Sugar | 15 tbs. Sugar |

100 teasp. Cinnamon | 2.5 teasp Cinnamon | 1.5 teasp Cinnamon |

140 cups of Pumpkin | 3.5 cups of Pumpkin | 4 cups of Pumpkin |

**Helena** and **George** both provided clear explanations. George explained: "To find out if Peter had enough to make 2 pies I divided each of the ingredients by 40. For the 10 dozen eggs I first multiplied 10 by 12, because dozen means 12. Then I divided the answer by 40.

10 X12 = 120.

120 / 40 = 12 / 4 = 3

Peter had 2 eggs but he needed 3 eggs so he had to buy 1 more egg.

To find out how many litres of condensed milk was needed, I first converted the litres of condensed milk into millilitres of condensed milk. Then I divided the answer by 40 again.

27litres X 1000 = 27,000ml

27,000ml / 40 = 675ml

Peter had 666ml but he needed 675ml so he needed to buy 9ml of condensed milk.

To find out how many tablespoons of sugar Peter needed I just divided the amount for 80 pies by 40.

480 / 40 = 12 tablespoons of sugar.

Peter had 15 tablespoons of sugar so he had 3 more.

To find out how many teaspoons of cinnamon, I divided the original amount again by 40.

100 / 40 = 10 / 4 = 2.5 teaspoons of cinnamon.

Peter had 1.5 teaspoons of cinnamon, so he needed to buy 1 more teaspoon of cinnamon.

Finally, to find out how many cups of pumpkin were needed I divided 140 by 40.

140 / 40 = 14 / 4 = 3.5 cups of pumpkin.

Peter had 4 cups of pumpkin so he had 0.5 cups of pumpkin more than he needs".

## Teachers' Resources

**Why do this problem?**

### Possible approach

### Key questions

### Possible extension

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