Mixed numbers equation

4 5/9 is the same as the sum of 2 1/3 and 5/6 times a number.

What is the number?

Enter your answer as a mixed number in simplest form in the box.

Final Answer:

x =  2 ²⁄₃ = 8/3

Step-by-step explanation:

$$\begin{gathered} a=4\frac{5}{9}=4+\frac{5}{9}=\frac{4\cdot 9+5}{9}=\frac{36+5}{9}=\frac{41}{9}=4\frac{5}{9}\doteq 4.5556 \\ b=2\frac{1}{3}=2+\frac{1}{3}=\frac{2\cdot 3+1}{3}=\frac{6+1}{3}=\frac{7}{3}=2\frac{1}{3}\doteq 2.3333 \\ a=b+\frac{5}{6}\cdot x \\ a-b=\frac{5}{6}\cdot x \\ c=a-b=\frac{41}{9}-\frac{7}{3}=\frac{41}{9}-\frac{21}{9}=\frac{41-21}{9}=\frac{20}{9}=2\frac{2}{9}\doteq 2.2222 \\ x=\frac{6}{5}\cdot c=\frac{6}{5}\cdot \frac{20}{9}=\frac{6\cdot 20}{5\cdot 9}=\frac{120}{45}=\frac{8}{3}=2\frac{2}{3}=2.6667 \end{gathered}$$

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