Princeton Review
A cement mixture is composed of 3 elements. By weight, 1/3 of the mixture is sand, 3/5 of the mixture is water, and the remaining 12 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?
A. 4
B. 8
C. 36
D. 60
E. 180
OA E
A cement mixture is composed of 3 elements. By weight, 1/3 of the mixture is sand, 3/5 of the mixture is...
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Given that
Sand composition in the mixture = \(\frac{1}{3}\)
Water composition in the mixture = \(\frac{3}{5}\)
Let the gravel composition be x
We know that the entire sum of the 3 elements needs to be 1
i.e.,
\(\frac{1}{3}\) + \(\frac{3}{5}\) + x =1
or
x= 1- \(\frac{1}{3}\) - \(\frac{3}{5}\)
x = \(\frac{15\ -5-9}{15}\)
x= \(\frac{1}{15}\)
We now know that there is \(\frac{1}{15}\) of mixture is composed of gravel
Let Y be the total weight of the mixture
It's given that
xY=12 pounds
Substituting x= \(\frac{1}{15}\)
\(\frac{1}{15}\) *Y=12
Y=12*15= 180 pounds
Hence the total weight of the mixture is 180 pounds
Sand composition in the mixture = \(\frac{1}{3}\)
Water composition in the mixture = \(\frac{3}{5}\)
Let the gravel composition be x
We know that the entire sum of the 3 elements needs to be 1
i.e.,
\(\frac{1}{3}\) + \(\frac{3}{5}\) + x =1
or
x= 1- \(\frac{1}{3}\) - \(\frac{3}{5}\)
x = \(\frac{15\ -5-9}{15}\)
x= \(\frac{1}{15}\)
We now know that there is \(\frac{1}{15}\) of mixture is composed of gravel
Let Y be the total weight of the mixture
It's given that
xY=12 pounds
Substituting x= \(\frac{1}{15}\)
\(\frac{1}{15}\) *Y=12
Y=12*15= 180 pounds
Hence the total weight of the mixture is 180 pounds