Question 1038894: Hey, I need help with this linear equation problem.
A weightlifter adds certain number of equally wighted plated to the barbell. The weighed plates are identical to one another.
If the total mass of the barbell and plates equal 60kg, and if each side of the barbell has the same number of plates, then one weighed plate could have a mass of_______?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the equation that i came up with is as follows:
t = b + 2*n*p
t is the total weight.
b is the weight of the barbell by itself with no plates added to it.
n is the number of plates on each side of the barbell.
p is the weight of each plate.
since you need 2 sides to the barbell, then n*P is multiplied by 2 to get 2*n*p.
as an example:
assume t = 60
assume b = 0 (not realistic, but useful for this example).
formula becomes 60 = 0 + 2*n*p
divide both sides of this equation by 2 to get 30 = n*p.
you can solve for p in this equation by doing the following:
start with 30 = n*p
divide both sides of this equation by n to get 30/n = p.
the value of p is dependent on the value of n.
if n = 1, then p = 30.
if n = 2, then p = 15.
if n = 3, then p = 10.
if n = 4, then p = 7.5
etc.....
what you do know is that, assuming the weight of the barbell is equal to 0, then the weight of each plate can't be greater than 30.
since the weight of the barbell will never be equal to 0, thsi a more realistic equation would be as follows:
60 = b + 2*n*p
you need to determine the weight of the barbell.
assuming the weight of the barbell is 10, then the formula becomes:
60 = 10 + 2*n*p
subtract 10 from both sides of this equaiton to get 50 = 2*n*p
divide both sides of this equation by 2 to get 25 = n*p.
you can now solve this equation for p to get p = 25/n.
if n = 1, then p is equal to 25.
if n = 2, then p is equal to 12.5.
if n = 3, then p is equal to 8 and 1/3.
if n = 4, then p is equal to 6.25
if n = 5, then p is equal to 5.
assuming n = 5 and b = 10 and p = 5, then the formula becomes:
60 = 10 + 2*5*5 which becomes 60 = 10 + 2*25 which becomes 60 10 + 50 which becomes 60 = 60.
the formula works IF you assume that each of the plates is identical in weight to each of the other plates.
since this doesn't ordinarily happen in real life, then you can have a mix of different plate sizes on each side of the barbell.
for example, assuming the barbell is 10 pounds again, then you need 25 pounds of plates on each side of the barbell.
each side could have one 25 pound plate.
each side could have two 10 pound plates and 1 five pound plate.
each side could have five 5 pound plates.
two 10 pound plates and two 2.5 pound plates.
any number of combinations of plates on each side are possible depending on the weight of each plate that is on hand.
a more realistic equation would therefore be:
t = b + 2*p
t equals the total weight of the barbell plus the plates.
b equals the weight of the barbell.
p equals the total weight on each side of the barbell.
in this particular case, assuming the total weight was 60 pounds and the weight of the barbell was 10 pounds, the equation would become:
60 = 10 + 2*p
solve for p to get p = 50/2 = 25.
you would know that you would need a total of 25 pounds of plates on each side of the barbell.
you would then need to see what possible combinations you could use, depending on the weights of each plate that you has on hand.
if you had 25 pound plates, then you would need 1 of them on each side.
if you had 5 pound plates, then you would need 5 of them on each side.
if you had 10 pound plates and 5 pound plates, then you could have two 10 pound plates and one 5 pound plate on each side.
another complication would be the length of the bar on each side of the barbell.
if it can hold a maximum of 4 plates, then five 5 pound plates on each side would not fit.
if this is a problem for school, then the question does not seem to be worded very well and leads to all sorts of complications that you could not be expected to know, depending on what grade you are in.
if this is a quesiton that you just wanted to know for you own personal education, then this answer should give you some clue as to the realistic complexities involved.
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