# How many eggs?

## Problem

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs.

Jack had one less than Peter.

Peter had 5 less than Melanie.

Amil had half as many as Melanie.

Peter had 2 more than Amil.

How many eggs did each person have?

## Student Solutions

Lots of people sent in correct solutions for this one. There are many ways to work through this problem, so the best solutions included a description of the thinking that was used.

The answer is:

Amil - 7 eggs

Jack - 8 eggs

Peter - 9 eggs

Melanie - 14 eggs (Lucky girl!)

__Solution 1__

Abbie (St Peters School, St Albans UK) first used logic to work out which child had the most eggs, then used this as a starting point for using the numbers. Abbie said:

I worked it out first by doing this ...

Jack < Peter *(has less than)*

Peter < Melanie

Amil < Melanie

Amil < Peter

Then you can see that the people with most eggs are Melanie and Peter, but Peter has five less than Melanie, so Melanie has most eggs. Then you can do this - Melanie has most, Peter has five less than her (Melanie -5), Jack has 1 less than Peter (Melanie -6), and Amil has 2 less than Peter (Melanie -7). As we know that Amil has half as many eggs as Melanie then Melanie must have 14 eggs, and then you can work the rest out! I checked by adding all the eggs together and they make 38.

__Solution 2__

Timothy used the first letter of each child's name, together with the numbers given in the clues, to make some equations. Timothy said:

To work out the puzzle I used Algebra.

J + 1 = P

P + 5 = M

M/2 = A

A + 2 = P

I knew that the two 'P's (standing for Peter) must equal the same so I guessed this,

6 = J, so J + 1 = P so P = 7 so

7 + 5 = 12 so M = 12 so

12/2 = 6 so A = 6 so

6 + 2 = 8 so P = 8

The guess was wrong as Peter is 7 and 8.

8 = J so J + 1 = P = 9

P + 5 = 14 = M

M/2 = 7 = A

A + 2 = 9 = P

As P are now the same, all the numbers were added up to show

8 + 9 + 14 + 7 = 38 so

Peter had 9 eggs

Melanie had 14 eggs

Jack had 8 eggs

Amil had 7 eggs

__More Solutions__

Correct solutions were also sent in by:

Susannah (Headington Junior School)

Laura (All Saints School, Whiteparish)

Josh (Amptil)

William, Byron & Kerry (Downing Primary, Ipswich)

Harry (St Peters College, Adelaide, Australia)

Mark (St Johns, Walsall Wood)

Lijun (Singapore)