maths problem

[user789653241]

I came across this maths word problem and cannot solve it.

Q: Average test score for 3 children C, D, E was 2 point higher than average for 5 children A, B, C, D, E.
Sum of scores for child A and child B is 160.
What is the average score for all 5 children, A, B, C, D, E.

It was from my native country's grade 5 question, so meant for 10/11 years olds, so assume no algebra should be used. I haven't got a clue even using algebra either...
Can anyone help, please? Am I thinking too much?

I can solve it with algebra.

A + B = 160
and
(A + B + C + D + E)/5 = x

so other words (160 + C + D + E)/5 = x

(C + D + E)/3 = x + 2

rearranging (C + D + E) = 3(x +2)

so in other words

(160 + 3(x+2))/5 = x

multiplying both sides by 5

(160 + 3(x+2)) = 5x

getting rid of that second pesky bracket

160 + 3x + 6 = 5x

simplifying by adding the plain numbers and sorting out the factors

166 = 2x

divide both sides by 2

x = 83 (the average score of A,B,C,D,E is 83)

Thank you Wonderflonium. Glad to know the answer!

Ideally, it needs to be done without algebra, since it's arithmetic question for elementary(primary) school aged children.
Any idea how, anyone?

You'd have to use "guess and check" if you couldn't use algebra, with 80 (average of a & b) as a rough starting point.

So pick a number near 80, multiply it by 5, subtract 160 from that total, (which gives you c+d+e) divide that number by 3 (which gives you the average of c, d and e) and if the answer is 2 more than your original number, that was the right answer.

Obviously if you had the wrong answer keep trying until you find the number that works.

Does that make sense? It's the kind of thing my 11 year old did in maths competitions he was in here, so tricky for general school stuff (in Australia anyway!).

Assuming that the children have been working in averages rather than algebra?
The five scores added together need to be divisible by 5.
The sum of scores C,D and E need to be divisible by 3.
And the average of scores C,D and E must be (a bit) higher than the average of A and B if they are going to increase the overall average by 2 points.
From there, it should be straightforward-ish?
There are only a couple of possibilities, so they should be able to solve it by using a bit of trial and error I think? The algebra is neater, but there is definitely more than one way to approach the problem!

Thank you, both. Sounds simple, but my head got really muddled up!
After reading Quod 's post, I thought yeah, that should be it, but still get confused to work it out properly. (I am not a naturally maths person.)

True mathematician maybe able to solve it without any problem, but I doubt my ds, who is quite good at maths will ace this.( I haven't given him this question yet.)

Ok so let's say you guess the answer, which is the average of a, b, c, d and e might be 82.

Multiply that by 5 to get the sum of a b c d and e, so 410.

Subtract 160 (a+b) from that, leaving you with c+d+e=250

Divide this by 3 to get the average of c d and e, oops 250 is not divisible by 3, so 82 can't be the answer.

Try the same process with 83 as a starting point and the average of c d and e comes to 85, which satisfies the question. So 83 is the answer.

Algebra is a much more elegant way to do it though!

Love these kind of questions. Love MN more for a clear answer!

Thanks again, Quod.

Yes, I do prefer algebra!
But it must be important for kids to go through these trial and error methods to learn problem solving/thinking process/patience!

My year 5 (age 9) is doing algebra at school at the moment. It goes right over my head. I didn't do it till I got to secondary and I never understood it then,guess that's why I only did a CSE in arithmetic . Reading Wonders reply just had me confused even more.

Those of you that can understand it I salute you.

You're welcome!

My DS found that method frustrating and time-consuming so I taught him some simple algebra to use in the competition, which his logical little brain much preferred!