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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?

 Jan 26, 2022
 #1
avatar+361 
+1

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?.....

 Jan 27, 2022
 #2
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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

 Jan 27, 2022
 #3
avatar+231 
+3

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

 Jan 28, 2022

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