Jim weighs 30 pounds less than Tom, and together they weigh 210 pounds. Let n Tom's weight in pounds. What would be the equation that expresses the total of Jim's and Tom's weights?

Mar 29, 2018

Jim and Tom's total weight is expressed by

$n + \left(n - 30\right) = 210$

and solving this equation tells us that Tom weighs 120 pounds, and Jim weighs 90 pounds.

Explanation:

If $n$ is Tom's weight, then Jim's weight is

$n - 30$

So an equation for their total weight would be

$n + \left(n - 30\right) = 210$

We could then continue to solve for $n$ to find Tom's weight

$\Rightarrow 2 n - 30 = 210$

$\Rightarrow 2 n - \cancel{30}$ $\textcolor{red}{+ \cancel{30}} = 210$ $\textcolor{red}{+ 30}$

$\Rightarrow 2 n = 240$

$\Rightarrow \frac{\cancel{2} n}{\textcolor{red}{\cancel{2}}} = \frac{240}{\textcolor{red}{2}}$

$\Rightarrow n = 120$

Tom weighs 120 pounds.

Jim's weight is then

$n - 30$

$\Rightarrow \textcolor{red}{120} - 30$

$\Rightarrow 90$

Jim weighs 90 pounds.