Question

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

Answer 1

Just a way of thinking: looking for mental shortcuts.

`x=30`

Explanation:

`0.30=3xx1/10`

so `0.3(80)color(white)("dd")=color(white)("dd")3xx80xx1/10color(white)("dd")=color(white)("dd")3xx8color(white)("dd")=color(white)("dd")24`

`0.40(80)color(white)("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+0.6x=32+0.4x`

`0.6x-0.4x=32-24`

`0.2x=6`

`x=(6xx10)/(0.2 xx10)=60/2=30`