Math test 3

How many students took the math test if one third of them solved only some of the problems. A quarter of the remaining students did not solve a single problem and 75 students solved all the problems.

Final Answer:

n =  150

Step-by-step explanation:

$$\begin{gathered} a=\frac{1}{3}\doteq 0.3333 \\ b=(1-a)/4=(1-\frac{1}{3})/4=\frac{1}{6}\doteq 0.1667 \\ c=1-(a+b)=1-(\frac{1}{3}+\frac{1}{6})=\frac{1}{2}=0.5 \\ c\cdot n=75 \\ n=75/c=75/\frac{1}{2}=75:\frac{1}{2}=75\cdot \frac{2}{1}=\frac{75\cdot 2}{1}=\frac{150}{1}=150 \end{gathered}$$

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