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Question 1202330: Sarah had some money in the piggy bank. On Monday, she took out 2/5 of the money to buy a present. She had $78 left and she put it back into the piggy bank. On Tuesday, she took out 3/8 of the money to buy some story books. She had $28.80 left and she put it back into the piggy bank. After that, she found that there was $246.30 in the piggy bank. How much money did she have in the piggy bank at first?
Found 2 solutions by math_tutor2020, MathTherapy:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Answer: $450
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(3/8)*((3/5)x + 78) = amount withdrawn on Tuesday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 = 450
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(2/5)*450 = 180 dollars withdrawn on Monday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(3/8)*348 = 130.50 dollars withdrawn on Tuesday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.
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website!
Sarah had some money in the piggy bank. On Monday, she took out 2/5 of the money to buy a present. She had $78 left and she put it back into the piggy bank. On Tuesday, she took out 3/8 of the money to buy some story books. She had $28.80 left and she put it back into the piggy bank. After that, she found that there was $246.30 in the piggy bank. How much money did she have in the piggy bank at first?
Let initial amount in piggy bank be A
After taking out  , she had  remaining
Since the remainder from the  , was $78, then after placing the $78 back, there was  in the piggy bank
On Tuesday,  of remainder was taken out leaving  of remainder or 
After placing the $28.80 back into the piggy bank, she then had 
Since the final amount in the piggy bank was $246.30, we then get: 
3A = 1,740 - 390 -------- Multiplying by LCD, 8
3A = 1,350
Initial amount in piggy bank, or 
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