Joy and Hassan has a collection of 240 magnets at first. Then Hassan
borrowed 1/5 of the number of magnets that Joy had. Later, Hassan lent out
1/4 of the number of magnets that he had Joy. Finally, Joy gave 40
magnets to Hassan. In the end, Joy had 26 magnets fewer than Hassan.
How many magnets did Hassan have at first?
I assume all that lending and borrowing takes place between these two people.
at start:
Joy had x, and Hassan had y
x + y = 240 or y = 240 - x
first episode:
1/5 of x goes to y
joy now has (4/5)x, Hassan has y + x/5
2nd episode:
1/4 of hassan's goes to joy
joy now has (4/5)x + (1/4)(y + x/5)
hassan has (3/4)(y + x/5)
3rd episode:
40 from joy to hassad
joy now has (4/5)x + (1/4)(y + x/5) - 40
hassad now has (3/4)(y + x/5) + 40
final situation:
[ (3/4)(y + x/5) + 40 ] - [ (4/5)x + (1/4)(y + x/5) - 40 ] = 26
3y/4 + 3x/20 + 40 - 4x/5 - y/4 - x/20 + 40 = 26
each term times 20
15y + 3x + 800 - 16x - 5y - x + 800 = 520
10y - 14x = -1080
7x - 5y = 540
sub in y = 240 - x
7x - 5(240-x) = 540
7x - 1200 + 5x = 540
x = 145
y = 240-145 = 95
check my arithmetic