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

Oct 3, 2015

Mac's Mass is $55$ kg.

#### Explanation:

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

5kg more than 3 times $\textcolor{g r e e n}{\text{Mac's Mass}}$ is decreased by twice $\textcolor{g r e e n}{\text{his mass}}$, the result is 60kg
$\Rightarrow$5kg more than 3 times $\textcolor{g r e e n}{m}$ is decreased by twice $\textcolor{g r e e n}{m}$, the result is 60kg

5kg more than $\textcolor{red}{3 \text{ times } m}$ is decreased by $\textcolor{b l u e}{\text{ twice } m}$, the result is 60kg
$\Rightarrow$5kg more than $\textcolor{red}{3 m}$ is decreased by $\textcolor{b l u e}{2 m}$, the result is 60kg

$\textcolor{g r e e n}{5 \text{kg more than } 3 m}$ is decreased by $2 m$, the result is 60kg
$\Rightarrow$$\textcolor{g r e e n}{5 + 3 m}$ is decreased by $2 m$, the result is 60kg

$\textcolor{red}{\left(5 + 3 m\right) \text{ is decreased by } 2 m}$, the result is 60kg
$\Rightarrow$
$\textcolor{red}{\left(5 + 3 m\right) - 2 m}$, the result is 60kg

$\left(\left(5 + 3 m\right) - 2 m\right)$$\textcolor{b l u e}{\text{ the result is "60"kg}}$
$\Rightarrow$$\left(\left(5 + 3 m\right) - 2 m\right)$$\textcolor{b l u e}{= 60 \text{kg}}$

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

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

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