What is with everyone writing 30=0.75 and things like that? If you're going to write a full solution don't make it totally worthless and explain what you're doing. Why the hell euler's identity and differentiation is coming into this I have no idea. This is a GCSE-level question at most.
EDIT: I now realise that a couple of you are indeed trolling
OP even though we don't regularly write full solutions I feel I may have to stop you getting confused from the above posts.
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Right, OP, we can write the initial number of red apples as R and the initial number of green apples as G.
So to begin with we have a total number of R + G apples.
If we add 10 red apples, we now have (10 + R) + G apples, with 10 + R red apples and G green apples.
We know that 0.6*total apples = G so G = 0.6(10 + R + G) and then 0.4G = 0.6R + 6 - this is our first equation, we can make it look neater by multiplying by 5 to give 2G = 3R + 30
Then from the second part we now have R + (G + 30) apples - with R red apples and G + 30 green apples.
You are then told 0.75*total apples = G + 30 or: 0.75(R + G + 30) = G + 30
Rearranging that formula gives 0.25G = 0.75R - 7.5 multiply by 8 to give 2G = 6R - 60
So now we have 2 equations:
2G = 6R - 60 and 2G = 3R + 30
From this we know 6R - 60 = 3R + 30; 3R = 90, R = 30
Subbing this in either equation we get 2G = 120 and so G = 60 then finally R + G = 90