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Chocoholics

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

You answered this tricky question very well using several different methods. Jack from Beech Primary wrote :

Because Jim needs 50p more to buy the chocolate, we know the chocolate costs at least 50p.

I used trial and improvement to find the answer.

We said C is the chocolate bar, J is Jim and G is George.

If the chocolate (C) costs 100p, then Jim has 50p and George has 98p. But the total would be 148p and this is too much, because they say that Jim and George do not have enough money when it's put together.

This means the chocolate bar is less than 100p but more than 50p.

C J G Total
100p 50p 98p 148p Too much
70p 20p 68p 88p Too much
50p 0p 48p 48p Could be right
51p 1p 49p 50p Could be right
52p 2p 50p 52p Too much
53p 3p 51p 54p Too much

So the right answer is either 50p or 51p. If Jim definitely has some money, then the cost of the chocolate bar is 51p.

Well done, Jack. Luke from St. Nicolas Junior School, Newbury reasoned his way through the solution :

George needs 2p more, so Jim must have less than 2p because otherwise, he would have given George the 2p he needed. So I chose 1p for Jim. As Jim needed 50p more, the chocolate bar must cost 51p.

Jim Cost of chocolate bar George
1p 51p 49p

Add George's money and Jim's money, which is 50p, so they still don't have enough to buy the chocolate bar together. Another solution I found was:

Jim Cost of chocolate bar George
0p 50p 48p

This works but the words of the question make me think that Jim must have some money, that is 1p.

Very well explained, Luke. Finally, Mikey from Archbishop of York C of E School used algebra to arrive at his solution:

Let's say George has G pence then choc bar costs G+2 pence.
Say C = G + 2 or G = C - 2.
Similarly Jim has J pence and choc costs J + 50 pence.
Say C = J + 50 or J = C - 50.
If their total money is less than cost of a bar then G + J is less than choc bar.
So G + J < C which is the same as (C - 2) + (C - 50) < C.
This simplifies to 2C - 52 < C and further to C < 52.
So the choc bar costs less than 52p but George has 48p more than Jim.
So the only possibility is for George to have 49p, Jim 1p, their total is 50p and the choc bar must be 51p (as we showed above it must be less than 52p).

Another clear solution - fantastic!