SOLUTION: On Monday, John put some jellybeans in the jar. On Tuesday, Peter ate 1/3 of the jellybeans and John topped up the jar with another 60 jellybeans. On Wednesday, Peter ate 220 jelly

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: On Monday, John put some jellybeans in the jar. On Tuesday, Peter ate 1/3 of the jellybeans and John topped up the jar with another 60 jellybeans. On Wednesday, Peter ate 220 jelly      Log On


   

Question 1203538: On Monday, John put some jellybeans in the jar. On Tuesday, Peter ate 1/3 of the jellybeans and John topped up the jar with another 60 jellybeans. On Wednesday, Peter ate 220 jellybeans and John topped up the jar with another 60 jellybeans. The jar now has 5/9 of the number of jellybeans at the end of Tuesday. How many jellybeans were in the jar at the end of (a) Wednesday and (b) Monday?
Answer by math_tutor2020(3817) About Me  (Show Source):
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x = starting number of jellybeans on Monday
Count at end of day
Mondayx
Tuesday(2/3)x+60
Wednesday( (2/3)x+60 ) - 220 + 60
Thursday(5/9)*( (2/3)x+60 )

Equate the last two expressions.
Solve for x.
( (2/3)x+60 ) - 220 + 60 = (5/9)*( (2/3)x+60 )
(2/3)x - 100 = (5/9)*(2/3)x+(5/9)*(60)
(2/3)x - 100 = (10/27)x+(100/3)
27*( (2/3)x - 100 ) = 27*( (10/27)x+(100/3) )
18x - 2700 = 10x+900
18x-10x = 900+2700
8x = 3600
x = 3600/8
x = 450 is the starting amount on Monday
Since the jelly beans aren't eaten on Monday, it's the ending amount on Monday.

Let's find the amount at the end of Wednesday.
( (2/3)x+60 ) - 220 + 60
(2/3)x - 100
(2/3)*450 - 100
300 - 100
200


Answers:
Amount at end of Wednesday = 200
Amount at end of Monday = 450