Question

Marisa saved $500 to spend on a vacation. She will spend about $45 per day on her vacation, and she must have $70 left to pay for her bus ride home. What inequalities best represents the possible numbers of days, d, Marisa could be on vacation?

Answer 1

The total is 500

The amount spent per day (x number of days) is 45

The change left over must be 70 and nothing less than that. This means, greater than or equal to 70.

Therefore, the inequality to represent this is;

`\begin{gathered} 500-45x\ge70 \\ -45x\ge70-500 \\ -45x\ge-430 \\ \text{Divide both sides by -45} \\ x\leq(430)/(45) \\ x\leq9.555 \end{gathered}`

Please note that when dividing or multiplying an inequality by a negative number, the sign of inequality will flip to the reverse. Its an exception to the rule when solving inequalities.

Therefore, the result, x is less than or equal to 9.55 means that Marisa could spend 9.55 days or less. Ideally, since its not practical to start calculating 0.55 of a day on vacation, the answer simply means Marisa must spend 9 days on vacation in other to have a change of $70 left on her.