Together, Paul and Quincy weigh 357 pounds, Quincy and Ramon weigh 348 pounds, and Paul and Ramon weigh 337 pounds. How much does each weigh individually?

Question

Quizplus · Accepted Answer

Let's use algebra to solve the problem, where P is Paul's weight, Q is Quincy's weight, and R is Ramon's weight:
P + Q = 357
Q + R = 348
P + R = 337
We can solve this system of equations by adding the second and third equations to eliminate R:
Q + R + P + R = 685
P + Q + R = 357 + 348 + 337 = 1042
2R + P + Q = 685
We can then substitute the first equation into this equation to eliminate Q:
2R + 357 = P + Q
2R + 357 = 1042 - P
2R = 685 - P
R = (685 - P)/2
We can then substitute this into the second equation to solve for Q:
(685 - P)/2 + Q = 348
Q = 174 - P/2
We can then substitute both expressions for Q and R into the first equation to solve for P:
P + 174 - P/2 = 357 - (685 - P)/2
3P/2 + 174 = 1022 - P/2
5P/2 = 848
P = 169.6
Using these values, we can find Q and R:
Q = 184.2
R = 164.2
Therefore, the answer is C) Paul = 173 lb., Quincy = 184 lb. , Ramon = 164 lb. (rounded to the nearest tenth of a pound).

Together, Paul and Quincy Weigh 357 Pounds, Quincy and Ramon