Leonardo was given a new phone on his last birthday. His parents had told him it was for emergencies only, but they're suspicious that he has been secretly texting a girlfriend that he hasn't told them about. The plan they got costs $49.98 per month, plus 10 cents per text message. If the bill for this first year that Leonardo had his new phone was $612.96, how many text messages did Leonardo use per month, on average?
Hint
Notice that the bill, $612.96, is for the entire year, while the plan costs $49.98 a month. The equation to solve is 12(49.98) + 0.1x = 612.96, with x as the number of text messages sent.
Answer
Leonardo sent 132 text messages throughout the year. That isn't enough information for his suspicious parents to nail him for secret smooching, though.
Example 2
Mr. and Mrs. Smith get into their respective cars to go to work. (Not the Mr. and Mrs. Smith from the movie; there are no car chases or gunfire in this word problem.) They leave their house at exactly the same time, and Mr. Smith heads west at 60 mph, while Mrs. Smith heads east at 45 mph. How long does it take before they are 42 miles apart?
Hint
After 1 hour, they will be (60 + 45) = 105 miles apart from each other. So, the formula for distance = 105t.
Answer
It takes 0.4 hours, or 24 minutes, for them to be 42 miles apart.
Example 3
Batty old Ms. Beauregard has a lot of cats and birds in her house. (It's not the animals that qualify her as batty, though: she thinks Elvis is alive and living in her basement.) There are a total of 252 legs in her house, including her own pair, and thankfully each of those legs is attached to a living organism. The number of birds is 3 less than twice the number of cats. How many cats does Ms. Beauregard have?
Hint
If c = the number of cats, and b = the number of birds, then we have:
2 + 2b + 4c = 252
b = 2c – 3
Do you remember how to perform substitution? Hint hint.
Answer
There are 32 cats and 61 birds living in batty old Ms. Beauregard's house.
Example 4
The length of a rectangular shed is 3 times its width, while its area is 27 ft2. What are its dimensions? Just saying length and width won't count, smarty pants.
Hint
l = 3w
l × w = 27
Answer
The width is 3 ft and the length is 9 ft.
Example 5
Two mimes walk into a bar. One of them says, "Ouch." The other puts him in an invisible box and ships him to work in the mime pits under Kansas as punishment. Shipping costs a $10 flat fee, plus 75 cents for every pound the package weighs. The total cost of shipping was $107.50. How much does the unfortunate mime weigh?