Another Maths conundrum

[Westwoodho]

The end result is 60%. This is the result of 2 marks one weighted at 40% the other at 60% -how do I calculate the 2 original marks?
(I only got grade 1 CSE maths back in 1973 and this has flummaxed me!!)

[grasscarp]

100% = 60%, so 10% is 6. so 40% is 24 and 60% is 36. ?

[grasscarp]

Let's hope a real maths expert looks at this. I think my calculation is probably not right at all!

[Westwoodho]

Whether you're right or wrong thanks for taking the trouble to respond. I have a whole set of other figures tht I can test it out on so I#ll give it a go.

[gen2]

There is not just one solution to this problem. If you know the mark obtained in one test then you can calculate the mark required in the othe test to give the overall target grade.

You work out the relationship as follows:

Let x = mark out of 100 in the first test
Let y = mark out of 100 in the second test

Now 40% of x + 40% of y = 60
or 40x/100 + 60y/100 = 60

multiply throughout by 100
40x + 60y = 6000
4x + 6y = 600
2x + 3y = 300

Rearranging
x = (300 - 3y)/2

or
y = (300 - 2x)/3

Example sets of solutions:
x = 0, y = 100
x = 75, y = 50

[gen2]

I double-checked that and STILL a typo slipped through.

In the middle, it should say

Now 40% of x + 60% of y = 60
or 40x/100 + 60y/100 = 60