SOLUTION: A money box contained some money at first. A took 1/2 the amount of money and another $1500 from the box. After that, B took 1/4 of the remaining amount of money and another $850 f

Algebra.Com
Question 1207243: A money box contained some money at first. A took 1/2 the amount of money and another $1500 from the box. After that, B took 1/4 of the remaining amount of money and another $850 from the box. In the end, C took the rest of the money left in the box. Given that C took $1400, find the amount of money in the box at first.
Found 4 solutions by josgarithmetic, ikleyn, greenestamps, MathTherapy:
Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!


-

-----------MISTAKE IN SIGN OR OPERATION-- -----

-------THE REST OF THIS IS WRONG---------------



-




Answer by ikleyn(52851)   (Show Source): You can put this solution on YOUR website!
.


        The  "solution",  calculation and the answer    in the post by @josgarithmetic all are incorrect.

        I came to bring a correct solution,  which is below.




-





-






Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


This kind of problem is often solved more easily by working backwards, as described below.

C got $1400.

Just before that, B took $850; so before B took $850 the amount was $1400+$850 = $2250.

Just before that, B took 1/4 of the money; that means the $2250 was 3/4 of the money that there was before. So the amount of money before B took 1/4 of it was $2250*(4/3) = $3000.

Just before that, A took $1500; so before A did that the amount was $3000+$1500 = $4500.

And just before that, A took 1/2 of the initial amount; that means the $4500 left after he took 1/2 of the money was also 1/2 of the money. So the initial amount of money was $4500*(2/1) = $9000.

ANSWER: $9000

CHECK:
$9000 minus 1/2 of $9000 = $9000-$4500 = $4500
$4500-$1500 = $3000
$3000 - 1/4 of $3000 = $3000-$750 = $2250
$2250-$850 = $1400
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
A money box contained some money at first. A took 1/2 the amount of money and another $1500 from the box. After that, B took 1/4 of the remaining amount of money and another $850 from the box. In the end, C took the rest of the money left in the box. Given that C took $1400, find the amount of money in the box at first.

Let original amount be M
After A took  and another $1,500, amount remaining = 
After B took  and another $850, amount remaining = 
Now, with C taking the rest of the money - which happens to be $1,400 - we EQUATE the
2 remainders to get: 
                             3M = 8(3,375) ----- Cross-multiplying
         Original amount, or

RELATED QUESTIONS

Two boxes of men’s Old Navy shirts were received from the factory. Box 1 contained 25... (answered by greenestamps)
Kathleen had some money at first. She spent 1/5 of it on a watch and 2/3 of it on a... (answered by ikleyn)
A box contained 50Cents coins and 20 cents coins in the ratio 2:3.when I took out foor... (answered by josgarithmetic,ikleyn,MathTherapy)
Hi There are some 20c coins in box A and some 50c coins in box B . If 40 coins are... (answered by ikleyn)
Alice had twice as much money as Peter. After Alice spent 1/6 of her money and Peter... (answered by ikleyn)
Nico is saving for college. He invests some money at 9% and $1500 less than that amount... (answered by solver91311)
A box contains 65 coins, only dimes and nickels. The amount of money in the box is $5.40, (answered by ikleyn,ankor@dixie-net.com)
Joanie got money from her uncle on every birthday. The amount of money he gives her is... (answered by Cromlix)
Nathan had some money. He spent 1/8 of it on a T-shirt and 3/4 of the remainder on... (answered by josgarithmetic,MathTherapy)