Question 1202330
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Answer:  <font color=red size=4>$450</font>


Work Shown:
x = starting amount


(2/5)x = amount she withdraws on Monday
x - (2/5)x = (3/5)x = amount left in the piggy bank, before the $78 is added
(3/5)x + 78 = amount after the $78 is added


(3/5)x + 78 = starting amount for Tuesday
(3/8)*((3/5)x + 78) = amount withdrawn on Tuesday
(5/8)*((3/5)x + 78) = amount in the piggy bank before the $28.80 is added
(5/8)*((3/5)x + 78)+28.80 = amount in the piggy bank after the $28.80 is added


That final expression is set equal to 246.30 which is the amount she has in the piggy bank after all is said and done.


(5/8)*((3/5)x + 78)+28.80 = 246.30
(5/8)*(3/5)x + (5/8)*78+28.80 = 246.30
(3/8)x + 48.75 + 28.80 = 246.30
(3/8)x + 77.55 = 246.30
(3/8)x = 246.30 - 77.55
(3/8)x = 168.75
x = 168.75*(8/3)
x = <font color=red>450</font>



Check:
Start with $450
(2/5)*450 = 180 dollars withdrawn on Monday
450-180 = 270 dollars remain in the piggy bank
270+78 = 348 dollars at the end of Monday
Then,
(3/8)*348 = 130.50 dollars withdrawn on Tuesday
348-130.50 = 217.50 dollars remain
217.50+28.80 = 246.30 dollars in the piggy bank at the end of Tuesday
We have fully confirmed the answer is correct.
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