# How do you solve 0.30(80) + 0.60x = 0.40(80 + x)?

May 30, 2018

Just a way of thinking: looking for mental shortcuts.

$x = 30$

#### Explanation:

$0.30 = 3 \times \frac{1}{10}$

so $0.3 \left(80\right) \textcolor{w h i t e}{\text{dd")=color(white)("dd")3xx80xx1/10color(white)("dd")=color(white)("dd")3xx8color(white)("dd")=color(white)("dd}} 24$

$0.40 \left(80\right) \textcolor{w h i t e}{\text{d")=color(white)("d")4xx80xx1/10color(white)("d")=color(white)("d")4xx8color(white)("d")=color(white)("d}} 32$
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Putting it all together we have:

$24 + 0.6 x = 32 + 0.4 x$

$0.6 x - 0.4 x = 32 - 24$

$0.2 x = 6$

$x = \frac{6 \times 10}{0.2 \times 10} = \frac{60}{2} = 30$