Addition like multiplication

Algebra Level pending

What is the value of the number when added to 8 3 \dfrac{8}{3} gives the same result as when it is multiplied by 8 3 \dfrac{8}{3} ?


The answer is 1.6.

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3 solutions

Chew-Seong Cheong
Oct 26, 2020

Let the number be x x . Then

x + 8 3 = 8 3 x 3 x + 8 = 8 x 8 x 3 x = 8 5 x = 8 x = 8 5 = 1.6 \begin{aligned} x + \frac 83 & = \frac 83 x \\ 3x + 8 & = 8x \\ 8x - 3x & = 8 \\ 5x & = 8 \\ \implies x & = \frac 85 = \boxed{1.6} \end{aligned}

James Watson
Oct 26, 2020

x + 8 3 = 8 3 x 5 3 x = 8 3 x = 8 3 5 3 = 8 5 = 1.6 \begin{aligned} x+\frac{8}{3} &= \frac{8}{3} x \\ \implies -\frac{5}{3}x &= -\frac{8}{3} \\ \implies x &= \frac{-\frac{8}{3}}{-\frac{5}{3}} = \green{\boxed{\frac{8}{5} = 1.6}} \end{aligned}

Let the number be x x

x + 8 3 = x × 8 3 \rightarrow x + \frac {8}{3} = x × \frac{8}{3}
3 x + 8 = 8 x \rightarrow 3x + 8 = 8x
8 = 5 x \rightarrow 8 = 5x
x = 8 5 = 1.6 \rightarrow x = \frac {8}{5} = \boxed{1.6}


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