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 $20$ $20$ pounds, Ted weighs $40$ $40$ pounds, and Mike weighs $60$ $60$ pounds.

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

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

Ted weighs twice as much as Julie $\to T = 2 J$ $rarr T=2J$

Mike weighs three times as much as Julie $\to M = 3 J$ $rarr M =3J$

Together, they weigh 120 lbs $\to T + J + M = 120$ $rarr T + J + M = 120$

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

$T + J + M = 120$ $T + J + M = 120$

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

$6 J = 120$ $6J = 120$

$J = 20$ $J = 20$

Julie weighs $120 pounds$ $"120 pounds"$ .

Now put $20$ $20$ into the first equations:

$T = 2 J$ $T= 2J$

$T = 2 (20)$ $T= 2(20)$

$T = 40$ $T= 40$

Ted weighs $40 pounds$ $"40 pounds"$

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

$M = 3 J$ $M = 3J$

$M = 3 (20)$ $M = 3(20)$

$M = 60$ $M = 60$

Mike weighs $60 pounds$ $"60 pounds"$