<p>Please explain what I need to do here. I can't get this problem:
Three people, Alvarez, Baird and Curtis find a box of dollar bills and decide that each person will receive a share of the money based on the amount of work that each contributed to the search. Thus they decided that Alvarez is to receive ½ of the money, Baird 1/3 of the money and Curtis 1/6 of the money. They divide the entire amount of money only to find that each person does not have the correct share. Alvarez returns ½ of the money he took, Baird returns 1/3 of the money he took, and Curtis returns 1/6 of the money he took. After this returned money is divided equally among the three people, each person has his rightful share. Determine a possible amount of money that was found in the box and the amount that each person took originally.
Thanks</p>
<p>I can put you on the right track by giving you the answer and the way to get there. </p>
<p>To get there, you will have to covert the problem in sets of equations. By glancing at the problem, you should note that the answer should be a multiple of 6 (because of 1/2, 1/3, and 1/6). </p>
<p>For the first equations, assume the original quantities are labeled a, b, and c. After giving a portion of the money back, the equations should be
a - a/2
b - b/3
c - c/6</p>
<p>The total of the money given back is a/2 + b/3 + c/6 or 3a/6 + 2b/6 + c/6. Since each one gets 1/3 of that money, each gets (3a+2b+c)/18. Calling x the total money, final total can be expressed as</p>
<p>(a - a/2) + (3a+2b+c)/18 = x/2
(b - b/3) + (3a+2b+c)/18 = x/3
(c - c/6) + (3a+2b+c)/18 = x/6</p>
<p>convert again</p>
<p>9a/18 + (3a+2b+c)/18 = 9x/18
12b/18 + (3a+2b+c)/18 = 6x/18
15c/18 + (3a+2b+c)/18 = 3x/18</p>
<p>solve as </p>
<p>9a + 3a+2b+c = 9x
12b+ 3a+2b+c= 6x
15c + 3a+2b+c = 3x</p>
<p>From here, you have to play around and simplify the equations by elimination. For instance, you should get to</p>
<p>18b + c = 5x
12 b + 15 c = 3x
and accordingly 78 c = 6b or 13c = b</p>
<p>Replacing 13 c for b in another equation yields a value for x/c of 47. </p>
<p>Now, we have a value of 47 for x/c, but it needs to be a multiple of 6, so let's simply take c = 6 for x = 282. </p>
<p>Let's plug in the numbers 78 and 6 for b and c, and use 282 as total.</p>
<p>198* - 99 = 99 + 42** = 141 or 1/2 of 282<br>
78 - 26 = 52 + 42** = 94 or 1/3 of 282<br>
6 - 1 = 5 + 42** = 47 or 1/6 of 282 </p>
<p>Total money is 282
* 198 is the plug for 282 - 78 - 6.
**Money given back is 126, so 1/3 is 42</p>
<p>There is a way to solve this a bit faster, but this should be simpler to follow.</p>
<p>thanks xiggi
but I had figured it out just a little while before you did
but u did get the right answer
all u had to do was what amount did they originally take and u can just multiply by 47 to take out the denominator so ur left with $33 for A, $13 for B, and $1 for C
u didnt have to go as far as making the amount 282 like a lot of my other classmates did
im curious what the other way was
is it by any chance using matricies</p>