Wendy has 80 more stamps than Mary but 50 more stamps than Jean.
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?
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
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.
Reiny, you finished ahead of me; but i'm
glad we got the same answer!
To get the same answer is always a good thing.
I also like the way our methods followed parallel tracks.
To solve this problem, let's break it down step by step.
Step 1: Find Wendy's stamps.
Let's assume that Wendy has x stamps. From the given information, we know that Wendy has 80 more stamps than Mary, so Mary would have (x - 80) stamps. We also know that Wendy has 50 more stamps than Jean, so Jean would have (x - 50) stamps.
Step 2: Wendy gives half of her stamps to Mary.
Therefore, Wendy will give (1/2)x stamps to Mary, and her stamp count will decrease to (1/2)x stamps. At the same time, Mary's stamp count will increase to (x - 80) + (1/2)x stamps.
Step 3: Mary gives one-fifth of her stamps to Jean.
So, Mary will give (1/5)((x - 80) + (1/2)x) stamps to Jean, which means Jean's stamp count will increase to (x - 50) + (1/5)((x - 80) + (1/2)x) stamps. At this point, we know that Jean has 62 more stamps than Wendy, so we can set up an equation:
(x - 50) + (1/5)((x - 80) + (1/2)x) = (1/2)x + 62
Step 4: Solve the equation to find x.
Let's solve the equation to find the value of x, which represents the number of stamps Wendy had originally.
(x - 50) + (1/5)((x - 80) + (1/2)x) = (1/2)x + 62
Multiply both sides of the equation by 10 to eliminate the fractions:
10(x - 50) + 2(x - 80) + 5(1/2)x = 5(x + 124)
10x - 500 + 2x - 160 + 5x = 5x + 620
17x - 660 = 5x + 620
12x = 1280
x = 1280 / 12
x = 106.67
Since the number of stamps cannot be in decimal form, we can round it to the nearest whole number.
x ≈ 107
Therefore, Wendy originally had 107 stamps.
Step 5: Find Mary's stamp count after the exchange.
Mary's stamp count would be (x - 80) + (1/2)x = (107 - 80) + (1/2)(107) = 27 + 53.5 = 80.5
So, Mary has 80.5 stamps in the end.