Note, that I'm going to represent Tom, Jenny and Bob as the following Variables:
The Amount of Money Tom gets will be: T
The Amount of Money Jenny gets will be: J
The Amount of Money Bob gets will be: B
First let's set up an equation which will work for this problem....
For one the money will be distributed to all 3, and there will be none left over. So we can represent that with this equation:
T + J + B = $3680
Meaning that the amount of money Tom, Jenny, and Bob each got added together will yield us our total amount 3680.
We have too many variables as it is. So, we will need to keep going and find more information.
"Jenny receives THREE times as much as Bob" is a key phrase. It can be represented with the following equation:
J = 3*B
"Tom receives TWICE as much as Jenny" is another key phrase. That can be represented like this:
T = 2*J
Let's try to plug a few of these in here.
T + J + B = 3680
T = 2*J
Replace T in the equation with 2*J.
2*J + J + B = 3680
J = 3*B
Replace J in the equation with 3*B
2*J + 3*B + B = 3680
Hm, we still have a problem here, because we have a J left. BUT! We can replace that 2*J with 2*(3*B), because J = 3*B.
2*(3*B) + 3*B + B = 3680
6B + 3B + B = 3680
10B = 3680
B = $368
Take the equation we had before we changed 2*J to 2*(3*B), and sub in the value for B:
2*J + 3*B + B = 3680
2*J + 3*368 + 368 = 3680
2*J + 1104 + 368 = 3680
2*J + 1472 = 3680
2*J = 3680 - 1472
2*J = 2208
J = $1104
Now take the ORIGINAL equation we made, and substitute in all of the values we have found thus far!
T + J + B = $3680
T + $1104 + $368 = $3680
T + $1407 = $3680
T = $3680 - $1407
T = $2208
Let's check to see if this works by plugging all the values we have found into the equation(s)!
Remember:
T = $2208
J = $1104
B = $368
T + J + B = $3680
$2208 + $1104 + $368 = $3680
$3680 = $3680
It checks out!
Let's check the other equations!
J = 3B
$1104 = 3*$368
$1104 = $1104
That one checks out!
T = 2J
$2208 = 2*$1104
$2208 = $2208
That one checks out as well!
Looks like they all check out, so our answers are... :
T = $2208
J = $1104
B = $368
Tom got $2208, Jenny got $1104, and Bob got $368.
