Click here for the Problem Extension Worksheet version of the Problems of the Week.
Click here for a MS Word version of the Problems of the Week.

Lower Elementary:
Question: Irene bought 2 sweaters each costing $30. If she paid with a $100 bill, how much change would he get back?
Answer: $40
Solution: Each sweater costs $30. 30 doubled is 60, so both sweaters cost $60. If she paid with a $100 bill, then she will receive $100 – $60 = $40 in change.

Upper Elementary:
Question: Quinn is flying from Sacramento to New York City. The clocks in New York City are 3 hours ahead of Sacramento (for example, if it is 2 PM in Sacramento, then it is 5 PM in New York City). If Quinn’s flight leaves Sacramento at 10:00 AM and the flight is 4 and a half hours long, what time is it in New York City when he arrives?
Answer: 5:30 PM
Solution: Four and a half hours past 10:00 AM is 2:30 PM in Sacramento. Since New York City clocks are 3 hours ahead, we add another 3 hours. Three hours past 2:30 PM is 5:30 PM.

Middle School:
Question: Lisa is baking a variety of cookies to put in goody bags. In each goody bag, 1/2 are chocolate chip, 1/5 are white chocolate, and the remaining 3 cookies are sugar. How many of each cookie are in each goody bag?
Answer: 3 sugar, 2 white chocolate, 5 chocolate chip
Solution: First we need to find the fractional part the sugars represent in each goody bag. To do this, we will add the other parts together and subtract it from the whole. Using the Law of Sameness, we get: 1/2 + 1/5 = 5/10 + 2/10 = 7/10
Subtract 7/10 from the whole to get 3/10. The sugar cookies are 3/10 of the total cookies, so that means that for every tenth, we have 1 cookie.
1/5 = 2/10, so 1 × 2 = 2 white chocolate cookies
1/2 = 5/10, so 1 × 5 = 5 chocolate chip cookies

Algebra and Up:
Question: Bill and Darren are mowing lawns. Bill can mow a lawn in an hour. If Bill and Darren work together, they can finish 2 lawns in 1 hour and 12 minutes. How long would it take for Darren to mow one lawn by himself?
Answer: 90 minutes, or an hour and a half
Solution: One way to solve this problem is to set up proportions of work over time, or rates. If we add Bill’s and Darren’s rates together, we will get the rate if they work together. The numerator will represent the number of lawns (work) and the denominator will represent the time it takes. Together, they can do 2 lawns in an hour and 12 minutes, or 72 minutes. That fraction is 2/72 which reduces to 1/36. For Bill, he can do 1 lawn in an hour, or 60 minutes. We will use 60 minutes instead of 1 hour because their combined time is in minutes. His fraction is 1/60. We do not know how long it takes Darren to mow one lawn, so his fraction will be 1/x. Our equation turns into:
1/60 + 1/x = 1/36
Multiply everything by the least common multiple so we do not have to solve this equation with fractions. In this case, the LCM is 180x.
180x × (1/60 + 1/x) = 180x × (1/36)
3x + 180 = 5x
180 = 2x
90 = x
So it takes 90 minutes, or an hour and a half, for Darren to mow one lawn.