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 spends 17 1/2 hours a week on the four subjects?

Final Answer:

S =  3 ³⁹⁄₄₀ = 159/40 h

Step-by-step explanation:

$$\begin{gathered} M=5\frac{2}{5}=5+\frac{2}{5}=\frac{5\cdot 5+2}{5}=\frac{25+2}{5}=\frac{27}{5}=5.4\text{h} \\ N=3\frac{3}{4}=3+\frac{3}{4}=\frac{3\cdot 4+3}{4}=\frac{12+3}{4}=\frac{15}{4}=3.75\text{h} \\ T=4\frac{3}{8}=4+\frac{3}{8}=\frac{4\cdot 8+3}{8}=\frac{32+3}{8}=\frac{35}{8}=4.375\text{h} \\ x=17\frac{1}{2}=17+\frac{1}{2}=\frac{17\cdot 2+1}{2}=\frac{34+1}{2}=\frac{35}{2}=17.5\text{h} \\ x=S+M+N+T \\ S=x-M-N-T=\frac{35}{2}-\frac{27}{5}-\frac{15}{4}-\frac{35}{8}=\frac{700}{40}-\frac{216}{40}-\frac{150}{40}-\frac{175}{40}=\frac{700-216-150-175}{40}=\frac{159}{40}=\frac{159}{40}\text{h}=3\frac{39}{40}\text{h}=3.975\text{h} \end{gathered}$$

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