Problema Solution
a gym offers a variety of weights for use by its members. If there are 6 more 50-pound weights than 100-pound weights and 2 less than 6 times as many 20-pound weights as 100-pound weights, for a total of 2150 pounds, how many of each weight are there?
Answer provided by our tutors
let
x = the number of 20-pound weights
y = the number of 50-pound weights
z = the number of 100-pound weights
there are 6 more 50-pound weights than 100-pound weights
y = 6 + z
2 less than 6 times as many 20-pound weights as 100-pound weights,
x = 6z - 2
for a total of 2150 pounds
20x + 50y + 100z = 2150
by solving the system of equations
y = 6 + z
x = 6z - 2
20x + 50y + 100z = 2150
we find
x = 40 weights of 20-pounds
y = 13 weights of 50-pounds
z = 7 weights of of 100-pounds
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