SOLUTION: Batman, Robin, Superman, and the Joker shared $60. Batman received ½ of the total amount of money Robin, Superman, and the Joker received. Robin received 2/3 of the total amount

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Question 582054: Batman, Robin, Superman, and the Joker shared $60. Batman received ½ of the total amount of money Robin, Superman, and the Joker received. Robin received 2/3 of the total amount of money Superman and the Joker received. Superman received 3 times as much as the Joker. A) How much money did Batman receive? B) How much more money did Robin receive than the Joker?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Write an equation for each statement, and see what we have here:
Batman, Robin, Superman, and the Joker shared $60.
b + r + s + j = 60
:
Batman received ½ of the total amount of money Robin, Superman, and the Joker received.
b = .5(r+s+j)
multiply by 2
2b = (r+s+j)
:
Robin received 2/3 of the total amount of money Superman and the Joker received.
r = 2%2F3(s+j)
:
Superman received 3 times as much as the Joker.
s = 3j
:
A) How much money did Batman receive?
We can replace r+s+j with 2b in the 1st equation
b + 2b = 60
3b = 60
b = $20 for Batman
:
Now we know: r + s + j = 40
replace s with 3j
r + 3j + j = 40
r + 4j = 40
r = (40-4j)
:
Take the equation r = 2%2F3(s+j)
replace r with (40-4j), replace s with 3j
40-4j = 2%2F3(3j + j)
3(40-4j) = 2(4j); multiplied both sides by 3
120 - 12j = 8j
120 = 8j + 12j
120 = 20j
j = $6 for the poor Joker
:
r = 40 - 4(6)
r = $16 for Robin
:
B) How much more money did Robin receive than the Joker?
$10
;
:
Find s so we can check this out
s = 3(6)
s = $18 for Superman
:
20 + 16 + 18 + 6 = $60