Help please!

[11+ novice]

Pauline and Katherine together have £40 more than Julie. Pauline has £8 more than Katherine. If they have £480 altogether, how much do they each have?

Is there a simple way to do this question?

[Tagore]

The only way I know how to solve these sort of questions is by basic Algebra. I am sure there is an easier way, and I hope one of the erudites will enlighten us.

My method is as follows :-

Pauline and Katherine together have £40 more than Julie - this gives equation 1 : P + K - J = 40
Pauline has £8 more than Katherine - this gives the second equation : P - K = 8
They have £480 altogether - this gives the third equation : P + K + J = 480

If you write one equation above the other, it becomes clear that the (P + K) in equation 3 can be replaced by (40 + J) derived from equation 1. This will result a value of £220 for J. You will then be left with two simple equations which upon solving will result values of £134 for P and £126 for K.

[11+ novice]

Thanks Tagore.

I taught my DS the same method but found that it was too long and he would make silly errors. I just feel this was too complicated for 10 years old to grasp.

Anyone else have some simpler solution!

[First-timer]

Pauline and Katherine together have £40 more than Julie. Pauline has £8 more than Katherine. If they have £480 altogether, how much do they each have?

Is there a simple way to do this question?

Break it down into chunks.
P+K have £40 more than J. Total is £480. For these problems I usually advise using the halfway mark as a starting point. In this case £240. But they aren't equal shares. The difference is £40 so the larger share is £20 more than the halfway point and the smaller share £20 less. So J has £220 and the others share £260.
Second chunk.
P has £8 more than K. Total is £260. Halfway is £130. Bigger share is £4 more and smaller share is £4 less than this starting point. So P has £134 and K has £126.

Hope this helps.

[11+ novice]

Thank you for the reply First -timer.