If 5kg more then 3 times Mac's Mass is decreased by twice his mass, the result is 60kg. What's Mac's Mass?

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If 5kg more then 3 times Mac's Mass is decreased by twice his mass, the result is 60kg. What's Mac's Mass?

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Answer 1 · 2015-10-03T14:05:30

Mac's Mass is $55$ $55$ kg.

Explanation:

Let $m$ $m$ be Mac's Mass
and convert the description a bit at a time into algebraic form:

5kg more than 3 times $Mac's Mass$ $color(green)("Mac's Mass")$ is decreased by twice $his mass$ $color(green)("his mass")$ , the result is 60kg
$\Rightarrow$ $rArr$ 5kg more than 3 times $m$ $color(green)(m)$ is decreased by twice $m$ $color(green)(m)$ , the result is 60kg

5kg more than $3 times m$ $color(red)(3" times "m)$ is decreased by $twice m$ $color(blue)(" twice "m)$ , the result is 60kg
$\Rightarrow$ $rArr$ 5kg more than $3 m$ $color(red)(3m)$ is decreased by $2 m$ $color(blue)(2m)$ , the result is 60kg

$5 kg more than 3 m$ $color(green)(5"kg more than "3m)$ is decreased by $2 m$ $2m$ , the result is 60kg
$\Rightarrow$ $rArr$ $5 + 3 m$ $color(green)(5+3m)$ is decreased by $2 m$ $2m$ , the result is 60kg

$(5 + 3 m) is decreased by 2 m$ $color(red)((5+3m)" is decreased by "2m)$ , the result is 60kg
$\Rightarrow$ $rArr$
$(5 + 3 m) - 2 m$ $color(red)((5+3m)-2m)$ , the result is 60kg

$((5 + 3 m) - 2 m)$ $((5+3m)-2m)$ $the result is 60 kg$ $color(blue)(" the result is "60"kg")$
$\Rightarrow$ $rArr$ $((5 + 3 m) - 2 m)$ $((5+3m)-2m)$ $= 60 kg$ $color(blue)(=60"kg")$

So we have:
$(5 + 3 m) - 2 m = 60$ $(5+3m)-2m = 60$

Combining the $m$ $m$ terms on the left side:
$5 + m = 60$ $5+m = 60$

Subtracting $5$ $5$ from both sides:
$m = 55$ $m = 55$

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If 5kg more then 3 times Mac's Mass is decreased by twice his mass, the result is 60kg. What's Mac's Mass?

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