Let x be the amount the salesperson sells in merchandise so that her commission is 0.12x. Her earning a day plus the commission is equal to $76.88 so the equation is:

\(\displaystyle{50}+{0.12}{x}={76.88}\)

Subtract 50 from both sides:

\(\displaystyle{0.12}{x}={26.88}\)

Divide both sides by 0.12:

\(\displaystyle{x}=\frac{{26.88}}{{0.12}}\)

\(\displaystyle{x}={224}\)

So, the salesperson sold an amount of $224 in merchandise.

\(\displaystyle{50}+{0.12}{x}={76.88}\)

Subtract 50 from both sides:

\(\displaystyle{0.12}{x}={26.88}\)

Divide both sides by 0.12:

\(\displaystyle{x}=\frac{{26.88}}{{0.12}}\)

\(\displaystyle{x}={224}\)

So, the salesperson sold an amount of $224 in merchandise.