Posted by markmorse@nocharge.com (66.109.197.222) on October 11, 2003 at 02:47:52:
In Reply to: Boat Weight posted by on October 11, 2003 at 01:57:06:
This word problems relates the weights of three items: a boat, a motor, and a trailer. Let's assign variables to represent these three quantities.
B = Boat weight
M = Motor weight
T = Trailer weight
Now we can use the given information to write three equations. The weight of the motor plus 1500 pounds equals the weight of the boat.
B = M + 1500
The weight of the trailer plus 1900 pounds also equals the weight of the boat.
B = T + 1900
Five times the weight of the trailer equals the weights of the boat and motor combined.
5T = B + M
This problem only asks for B, so we don't need to find M or T. Here is one strategy: Solve the last equation for T. This will yield an expression containing B and M. Substitute this expression for T in the second equation. This will yield a new equation that contains only B and M. We can then subtract the first equation from it to eliminate M. Once we have the equation that contains only B, we can find the answer. Here are the steps, again:
[Solve the last equation for T. This will yield an expression containing B and M.]
5T = B + M
(Divide both sides by 5.)
T = (1/5)(B + M)
[Substitute this expression for T in the second equation. This will yield a new equation that contains only B and M.]
B = T + 1900
B = (1/5)(B + M) + 1900
(Eliminate the fraction by multiplying both sides by 5.)
5B = B + M + 9500
(Subtract B from both sides.)
4B = M + 9500
[We can then subtract the first equation from it to eliminate M.]
4B = M + 9500
1B = M + 1500
--------------
3B = 8000
[Once we have the equation that contains only B, we can find the answer]
B = 8000/3
B = 2666-2/3
The boat weighs 2,666 and 2/3rds pounds.
If you need more help with this problem, please explain what part(s) you don't understand.
~ Mark