Exercises

1. A taxi charges \($0.75\) per km plus a base fare of \($8\). What is the maxiumum distance that you can travel for \($20\)?
2. An elevator has a capacity of \(2500\) lbs. Marshall has loaded an elevator with \(10\) boxes, each weighing \(75\) kg, \(2\) dressers that each weigh \(100\) kg and a couch. If \(1~\text{kg}\approx2.2~\text{lbs}\), what is the maximum weight of the couch for the elevator to remain under capacity? Round your answer to two decimal places.
3. Lucia and Raphael were given an integer value. Lucia added \(6\) to the number and then divided the total by \(3\). Raphael added \(10\) to the number and then divided the total by \(4\). In the end, Lucia's result was smaller than Raphael's result. What is the greatest integer that they could have been given?
4. Solve the double inequality. 

   \(-9\lt\dfrac{x+6}{-3}\lt12\)

5. A 3D printing studio offers two pricing options for people wanting to use their printer.

   • Option 1: \($0.10\) per g of filament (printing material) used 
   • Option 2: \($5\) per month plus \($0.07 \) per g of filament used

   How much filament (in grams) should you use per month in order to make Option 2 cheaper than Option 1? Round your answer to two decimal places.

6. In the double inequality below, \(a\), \(b\), \(c\), and \(d\) are all unique integers between \(1\) and \(9\) inclusive. Find the values of \(a\), \(b\), \(c\), and \(d\) that give the widest range for the solution of \(x\).

   \(a\le\dfrac{b+x}{c}\le d\)