One day, Bianca withdrew 30% of the money in her account to

Question

One day, Bianca withdrew 30% of the money in her account to pay her son’s tuition. She then received a transfer of $4,500 for a translating job she had completed. The next day, she withdrew 20% of the money in her account to pay her daughter’s tuition and, minutes later, received another transfer of $4,500. If the balance in her account decreased by 35% over the two days and there were no other transactions in her account those days, how much did Bianca withdraw to pay for her daughter’s tuition?

A. $13,500
B. $15,500
C. $18,000
D. $20,000
E. $27,000

Show Answer

Official Answer

A

A. $13,500
B. $15,500
C. $18,000
D. $20,000
E. $27,000

paragw · Answer

Let initial total be 100x
son’s tuition fee = 30x; Remaining = 70x
4500 added to the account: (70x+4500)
Daughter’s tuition fee = 20% of (70x+4500) = 14x + 900; Remaining = 56x + 3600
4500 added to the account: (56x + 8100)
& this amount is equal to 65x (given in the question stem)
56x + 8100 = 65x
x = 900
Daughter’s tuition fee = 14x + 900 = 14(900) + 900 = 13500
Hence,  A

findingmyself · Answer

Let the amount in account be T
After 30% withdrawl, balance is 0.7T

After recieving $4500, balance is 0.7T+$4500

Then she paid 20% of (0.7T+$4500) for Tution fee

Balance is 0.8*(0.7T+$4500)

Now she recieved another $4500

New balance is 0.8*(0.7T+$4500)+$4500

This new balance account for 65% of her initial balance (35% decreased means that the initial balance has now become 0.65T)

0.65T= 0.8*(0.7T+$4500)+$4500

Solving for T we get T=90,000

Now trap answer which i choose was 20% of 90,000 which is $18000 WRONG!!

What we need is 20% of (0.7T+$4500) which is equal to $13500

kevincan · Answer

Nasty trap answers

jytron · Answer

Nice question! Very easy to fall into the trap at the end if you rush.

I used algebra with decimals:
Let $x$ be the starting balance.

1. After 30% withdrawal: $0.7x$2. + $4500: $0.7x + 4500$
2. Withdraws 20% (so 80% remains): $0.8(0.7x + 4500) = 0.56x + 3600$4. + another $4500: $0.56x + 8100$

Overall balance dropped by 35%, so remaining is $65\%$ of $x$:
$0.56x + 8100 = 0.65x$
$0.09x = 8100$
$x = 90,000$

The question asks for her daughter's tuition, which is 20% of the balance at that moment ($0.7x + 4500$), not 20% of the initial balance!

$0.2 \cdot (0.7 \cdot 90000 + 4500)$
$= 0.2 \cdot (63000 + 4500)$
$= 0.2 \cdot 67500 = 13,500$

Option A

One day, Bianca withdrew 30% of the money in her account to

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