Wendy has 80 more stamps than Mary but 50 more stamps than Jean.

Question

Wendy gives 1/2 of her stamps to Mary. Then Mary gives 1/5 of her stamps to Jean. If Jean has 62 more stamps than Wendy, how many stamps does Mary have in the end?

Answer 1

right now:
Mary ---- x
Wendy -- x+80
Jean --- x+30

after giveaway:
Wendy --- (x+80)/2
Mary now has x + (x+80)/2
= (3x + 80)/2
but she gives (1/5)of that to Jean
Mary is left with :
(4/5)(3x+80)/2
and Jean now has (1/5)(3x+80)/2 + x+30
= (13x+380)/10

so now Jean has 62 more than Wendy
(13x + 380)/10 = 62 + (x+80)/2
times 10
13x + 380 = 620 + 5x + 400
8x = 640
x = 80

Now Mary now has (4/5)((3x+80)/2 = (4/5)(240+80)/2 = 128

check:
at the start
Mary had 80
Wendy had 160
Jean had 110

Wendy gave 1/2 to Mary:
Mary now has 160
Wendy has 80
Jean has 110
Now Mary gives 1/5 of hers to Jean
(Mary gives 32 to Jean)
Mary has 160-32 = 128
Wendy still has 80
Jean has 110+32 = 142

Does Jean have 62 more than Wendy????
142-80 = 62
YEAHHHH

Answer 2

Mary = X Stamps.
Wendy = X + 80
Jean = (X+80)-50 = X + 30

After Transactions:
Mary= X + (X+80)/2 = (3X/2+40).
Mary = 4/5(3X/2+40) = 6X/5+32
Wendy = (X+80)/2
Jean = (X+30)+3X/10+8=13X/10+38

Jean = (13X/10+38)=(X/2+40)+62
13X/10-X/2 = 62+40-38 = 64
13X/10-5X/10 = 64
8X/10 = 64
8X = 640
X = 80 Stamps.

Mary = 6X/5 + 32 = 480/5 + 32=128 Stamps
in the end.

Answer 3

Reiny, you finished ahead of me; but i'm
glad we got the same answer!

Answer 4

To get the same answer is always a good thing.
I also like the way our methods followed parallel tracks.