Ted weighs twice as much as Julie. Mike weighs three times as much as Julie. Together, Ted, Mike, and Julie weigh 210 lbs. What is the weight of each person?

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Answer 1 · 2018-04-01T12:10:20

Julie weighs #20# pounds, Ted weighs #40# pounds, and Mike weighs #60# pounds.

Let's give Ted, Julie, and Mike their own variable:
#"Ted" = T#
#"Julie" = J#
#"Mike" = M#

Now let's turn each of the pieces of information into a math equation:

Ted weighs twice as much as Julie #rarr T=2J#

Mike weighs three times as much as Julie #rarr M =3J#

Together, they weigh 120 lbs #rarr T + J + M = 120#

We can now substitute the first two equations into the last one, and solve it for Julie's weight:

#T + J + M = 120#

#(2J) + J + (3J)= 120#

#6J = 120#

#J = 20#

Julie weighs #"120 pounds"#.

Now put #20# into the first equations:

#T= 2J#

#T= 2(20)#

#T= 40#

Ted weighs #"40 pounds"#

Last step! Put #20# into the middle equation and solve for Mike's weight.

#M = 3J#

#M = 3(20)#

#M = 60#

Mike weighs #"60 pounds"#