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?

Question

Hazel Anglin · Accepted Answer

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"#

Jace Anderson · Answer

undefined Let's denote Julie's weight as $ J $ pounds.

According to the given information:
- Ted weighs twice as much as Julie, so Ted's weight is $ 2J $ pounds.
- Mike weighs three times as much as Julie, so Mike's weight is $ 3J $ pounds.
- Together, their total weight is 210 pounds.

So, we have the equation: 
$$ J + 2J + 3J = 210 $$

Combining like terms:
$$ 6J = 210 $$

Now, solve for $ J $:
$$ J = \frac{210}{6} = 35 \text{ pounds} $$

Therefore:
- Julie weighs $ 35 $ pounds.
- Ted weighs $ 2J = 2 \times 35 = 70 $ pounds.
- Mike weighs $ 3J = 3 \times 35 = 105 $ pounds.

Eva Abramson · Answer

undefined Let's represent Julie's weight as J lbs.

According to the given information:

Ted weighs twice as much as Julie, so Ted's weight is 2J lbs.

Mike weighs three times as much as Julie, so Mike's weight is 3J lbs.

Together, Ted, Mike, and Julie weigh 210 lbs, so the equation can be formed as:

J + 2J + 3J = 210

Combining like terms:

6J = 210

Divide both sides by 6:

J = 35

So, Julie weighs 35 lbs.

Ted weighs twice as much as Julie, so Ted weighs 2 * 35 = 70 lbs.

Mike weighs three times as much as Julie, so Mike weighs 3 * 35 = 105 lbs.