ABC26GN0793 · Decimal Fractions

$$\begin{aligned} & 2 \frac{1.5}{5}+2 \frac{1}{6}-1 \frac{3.5}{15}=\frac{x^{1 / 3}}{4}+1 \frac{7}{30} \\ & \Rightarrow \frac{11.5}{5}+\frac{13}{6}-\frac{18.5}{15}=\frac{x^{1 / 3}}{4}+\frac{37}{30} \end{aligned}$$ LCM of 5, 6 and 15 is 30. $$\begin{aligned} & \Rightarrow \frac{69+65-37}{30}=\frac{x^{1 / 3}}{4}+\frac{37}{30} \\ & \Rightarrow \frac{97}{30}=\frac{x^{\frac{1}{3}}}{4}+\frac{37}{30} \\ & \Rightarrow \frac{x^{1 / 3}}{4}=\frac{97}{30}-\frac{37}{30} \\ & \Rightarrow x^{1 / 3}=\frac{60}{30} \times 4 \\ & \Rightarrow x^{1 / 3}=8 \Rightarrow x=(8)^{3} \\ & \Rightarrow x=512 \end{aligned}$$ Hence, the number is 512.