# Cherry Buns

Sam's grandmother has an old recipe for cherry buns.

To make them, she weighs two eggs. Then she takes the same weight in flour, and in sugar and in butter. She mixes all this together and then she adds half the weight of the $2$ eggs in chopped glace cherries.

She has enough mixture to put $45$ grams in each of $12$ paper cake cases.

What was the weight of one egg?

How many "egg weights" were used in the recipe?

Why not find out how much mixture there is altogether?

There were several different ways to approach this problem. We received many solutions from children at Ardingly College who all tackled it in a similar way. Here is Jess' reasoning:

I wrote out the ingredients of the cherry buns and showed it like this:

egg = $2$

flour = $2$ eggs

sugar = $2$ eggs

butter = $2$ eggs

cherries = $1$ egg

total = $9$ eggsFirst I did $12 \times 45$g = $540$g (the total weight of the mixture)

$540/9$ = $60$g so one egg weighs $60$g.

Alistair from Histon Junior School wrote Jess' solution in a slightly shorter way:

If e = $1$ egg, there are $9$e in the recipe.

I multiplied $45$ by $12$ to get the total weight of mixture. $45x12 =540$

So an egg would be $540/9$ which is $60$, (then turn it into grams) making e = $60$g

Pupils from Oakwood Junior School did it a slightly different way. This is what Sophie wrote:

First I found out how much mixture there was by multiplying $45$g by $12$ paper cases. This gave me an answer of $540$g.

Then next I worked out how much of each ingredient there was in each case.

Eggs $10$g

Flour $10$g

Sugar $10$g

Butter $10$g

Cherries $5$g

Then I worked out how much mixture there was altogether for the 12 cakes:

Eggs $120$g

Flour $120$g

Sugar $120$g

Butter $120$g

Cherries $60$g

After this I halved the amount for the eggs and this gave me $60$g for one egg.

Davis from Berkeley Preparatory School used a trial and improvement approach:

First, my teacher and I found out how many grams the batter weighed by multiplying $45$grams times $12$ paper cake cases.

That means the total batter weighed $540$ grams.

Then, we wrote a formula:

Eggs + flour + sugar + butter + cherries = $540$ grams.

Since the eggs, flour, sugar, and butter all weighed exactly the same, at first we guessed that each ingredient weighed $100$ grams.

That would mean $100$g + $100$g + $100$g + $100$g + cherries (which weigh as much as half of the eggs...which would be $50$g)

However, when we added that together, it only equalled $450$g.

That told me that each ingredient had to weigh more than $100$ grams. So I decided to try $120$ grams.

$120$g + $120$g + $120$g + $120$g + cherries ($60$g) = $540$grams

Now that I know that TWO eggs equals the same as $120$g, ONE egg would equal $60$ grams.

Thank you Davis. Beth, Jennie and Henry found another way to answer the problem:

We set about solving it like this:

She put $45$g in each of $12$ cake cases. That is $12 \times 45$g = $540$g.

So the total mixture weighs $540$g.

Then we listed the ingredients:

$2$ eggs

flour

sugar

butter

glace cherries

The first $4$ weigh the same but the last one weighs only half.

So we need $540/4.5$. This is the weight of each of the first four ingredients.

$540/4.5$ = $120$ (we found this out by trial and improvement)

So $2$ eggs weigh $120$g and the weight of one egg is $60$g.

We checked our solution by writing out the ingredient list again with the weights and checking that the total was $540$g.

Thank you to everyone.