Problem Solving

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

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