5 2/5

5 2/5 hours a week  mathematics,  3 3/4 hours a week   Natural sciences, 4 3/8 hours a week  Technology . how many hours does  he spend on social sciences if he spend 17 1/2 hours a week for the four subject?

Correct answer:

S =  3.975 h

Step-by-step explanation:

$$\begin{gathered} M=5{\displaystyle \frac{2}{5}}=5+{\displaystyle \frac{2}{5}}={\displaystyle \frac{5\cdot 5+2}{5}}={\displaystyle \frac{27}{5}}=5.4\text{ h } \\ N=3{\displaystyle \frac{3}{4}}=3+{\displaystyle \frac{3}{4}}={\displaystyle \frac{3\cdot 4+3}{4}}={\displaystyle \frac{15}{4}}=3.75\text{ h } \\ T=4{\displaystyle \frac{3}{8}}=4+{\displaystyle \frac{3}{8}}={\displaystyle \frac{4\cdot 8+3}{8}}={\displaystyle \frac{35}{8}}=4.375\text{ h } \\ x=17{\displaystyle \frac{1}{2}}=17+{\displaystyle \frac{1}{2}}={\displaystyle \frac{17\cdot 2+1}{2}}={\displaystyle \frac{35}{2}}=17.5\text{ h } \\ x=S+M+N+T \\ S=x-M-N-T=17.5-5.4-3.75-4.375={\displaystyle \frac{159}{40}}\text{ h}=3\frac{39}{40}\text{ h}=3.975\text{ h} \end{gathered}$$

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