Chocoholics

'Chocoholics' printed from https://nrich.maths.org/

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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!