A one-way ticket costs $2. A 30-day pass costs $50. What's the minimum number of rides you will need to take every month so that the 30-day pass is strictly cheaper per ride? Give the rationale and then the answer.
Let's think step by step. For the 30 - day pass to be cheaper, then the average fare should be cheaper than the $2 one - way ticket. If the 30 - day pass costs $50, then I should take at least $50 / $2 = 25 rides to pay the same as a one - way ticket. However, given that we want the 30 - day pass per ride to be strictly cheaper we should ride at least 25 + 1 = 26 times.. The answer is: 26.

A laboratory has 22 beakers of liquid in a fume hood, and 8 of the beakers have copper ions in them. Adding three drops of a solution will turn the liquid in a beaker blue if there are copper ions present. If the beakers are tested one by one for copper ions and 45 drops are used before all 8 beakers with copper ions are found, how many beakers without copper ions were tested? Give the rationale and then the answer.
Let's think step by step. There were 45 / 3 = 15 beakers tested to find all the beakers with copper ions. Thus, 15 - 8 = 7 beakers without copper ions were tested.. The answer is: 7.

Josh has 100 feet of rope. He cuts the rope in half, and then takes one of the halves and cuts it in half again. He grabs one of the remaining pieces and cuts it into fifths. He's stuck holding one length of the rope he's most recently cut. How long is it? Give the rationale and then the answer.
Let's think step by step. John starts with 100ft of rope that he cuts in half, meaning he has 100 / 2 = 50 - foot sections of rope. He then takes one of these sections and cuts it in half again, leaving him with two 50 / 2 = 25 - foot sections of rope. He then takes one of these sections and cuts it into fifths, leaving him with 25 / 5 = 5 foot sections of rope, one of which he is now holding.. The answer is: 5.