Question

A taco stand sells tacos for $3.25 each. The stand’s expenses for the day are $210. Write an inequality to represent the amount of tacos they need to sell per day to make a profit, and then solve the inequality.

Answer 1

To make a profit, they need to sell enough tacos to pay their expenses AND have some money left over. So, we can write that as;
\[3.25x >210\]
Where x represents the amount of tacos, 3.25 represents the cost per taco, and 210 represents the expenses, to make a profit you need more than your expenses so the inequality sign is a greater than.

Now to solve the inequality, we need to divide both sides by 3.25 to get x alone;
\[\frac{ 3.25x }{ 3.25 }>\frac{ 210 }{ 3.25 }\]
\[x >64.61\]
But since you can't have .61 of a taco you round it up to 65.
The reason you don't just cut the extra .61 and leave it at 64 is because 64*3.25 only = 208, you need more than 210;
\[3.25\times65\approx211\]
Which is a $1 profit. So the taco stand will need to sell 65 tacos to make a profit.