# 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?

Apr 1, 2018

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

#### Explanation:

Let's give Ted, Julie, and Mike their own variable:
$\text{Ted} = T$
$\text{Julie} = J$
$\text{Mike} = M$

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

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

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

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

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

$T + J + M = 120$

$\left(2 J\right) + J + \left(3 J\right) = 120$

$6 J = 120$

$J = 20$

Julie weighs $\text{120 pounds}$.

Now put $20$ into the first equations:

$T = 2 J$

$T = 2 \left(20\right)$

$T = 40$

Ted weighs $\text{40 pounds}$

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

$M = 3 J$

$M = 3 \left(20\right)$

$M = 60$

Mike weighs $\text{60 pounds}$