Maths question(detail steps)

I spend $68 in buying apples at 5 for $3 and oranges at 5 for $2. I sell three-fourths of my apples and four-fifths of my oranges for $57, makig a profit of $5 on them. How many apples do I buy?
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Let a be the number of apples bought.
then a*3/5 is the money spent on apples.
money spent on oranges = (68-3a/5)
number of oranges = (68-3a/5)*5/2

3/4 of apples = 3a/4
4/5 of oranges = (68-a*3/5)*5/2 *4/5=2(68-3a/5)=136-6a/5

profit = 5$ = 57 - cost = 57 - 3a/4*3/5 - (136-6a/5)*2/5

Simplifying,
(3*a+260)/100=5
Solving, a=80

Answer: I bought 80 apples.

Check:
Number of oranges bought = (68-3a/5)*5/2 = 50
Sold 3/4*80=60 apples, 4/5*50=40 oranges.
Cost of 60 apples and 40 oranges=60*3/5+40*2/5=36+16 = 52$
So he made a profit of $57-$52=$5. OK