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# Cherry Buns

##### Age 7 to 11 Challenge Level:

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 = $9$ eggs

First 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.