Tom and Peter each picked some strawberries at a farm. Tom gave 1/3 of the strawberries he picked to Peter. Peter then gathered all the strawberries he had and gave 1/4 of them to Tom. Finally, Tom totalled up all his strawberries and gave 1/5 of them back to Peter. In the end, Tom had 32 strawberries and Peter had 56 strawberries. How many strawberries did each of them pick at first?
+364 work backwards
Tom:\(\frac{4}{5}=32\) \(\frac{1}{5}=8\) \(\frac{5}{5}=40\)
peter:\(\frac{6}{5}=56\) wait, then 5/5 wound equal \(\frac{4.\bar6}{5}\) huh?.....
2/5[2P + T]==56....................(1)
1/5[P + 3T]==32....................(2), solve for P, T
T==36 - what Tom started with
P ==52 - what Peter started with
+237 Let Tom have = x strawberries
Peter have = y straberries
When Tom gave 1/3
Tom = x - x/3 = 2x/3
Peter = y + x/3
When Peter gave 1/4
Peter = (y + x/3)3/4 = 3y/4 + x/4
Tom = 2x/3 + (y + x/3) 1/3 = 2x/3 + y/4 + x/12
When Tom gave 1/5
Tom = (3x/4 + y/4)4/5 = (3x + y)/5
Peter = ((3y + x)/4) + (3x/4 + y/4)1/5 => (4y + 2x)/5
Tom = (3x + y)/5 = 32
=> (1) --- 3x + y + 160
3x + y = 160
3(x + 2y = 140)
3x + y = 160
3x + 6y = 420
-------------------------
0 - 5y = -260
y = 52
Peter = (4y + 2x)/5 = 56
=> 4y + 2x = 280 (2)
2y + x = 140
3x + (52) = 160
3x = 108
x = 36
