**Lower Elementary:**

*Question: *Toby slept from 10:15 PM to 6:45 AM and then took a nap from 3:30 PM to 4:45 PM. How much of sleep did Toby get?

*Answer: *9 hours and 45 minutes

*Solution: *The elapsed time from 10:15 PM to 6:45 AM is 8 hours and 30 minutes. The elapsed time from 3:30 PM to 4:45 PM is 1 hour and 15 minutes. So that means to total time that Toby slept is 8 hours and 30 minutes + 1 hour and 15 minutes = 9 hours and 45 minutes.

**Upper Elementary:**

*Question: *For Hanukkah, Trevor needs the candles to burn for 90 minutes. If a candle burns 1 1/2 inches per 15 minutes, how long do the candles have to be to stay lit for 90 minutes?

*Answer: *9 inches

*Solution: *If 1 1/2 inches of candle can burn for 15 minutes, that means if we double both amounts that 3 inches of candle can burn for 30 minutes. If 3 inches of candle can burn for 30 minutes, that means if we triple both amounts 9 inches of candle can burn for 90 minutes. So the candles need to be 9 inches.

**Middle School:**

*Question: *Jessica, Kalvin, and Lloyd pitch in $30, $50, and $20 respectively to buy a bicycle. They then sold the bicycle for $80. How much should each of them get so that it is fair?

*Answer: *Jessica: $24, Kalvin: $40, Lloyd: $16

*Solution: *The bicycle originally costs $30 + $50 + $20 = $100. That means that Jessica should get 30 / 100 = 30% of the money back, Kalvin should get 50 / 100 = 50% of the money back, and Lloyd should get 20 / 100 = 20% of the money back. So, Jessica should get 30% of $80 = $24, Kalvin should get 50% of $80 = $40, and Lloyd should get 20% of $80 = $16.

**Algebra and Up:**

*Question: *Two apples and three bananas cost $4.20. Three apples and two bananas cost $4.55. How much do one apple and one banana cost separately?

*Answer: *One apple is $1.05 and one banana is 70¢

*Solution: *Let A be the cost of an apple and let B be the cost of a banana. Writing the problem as a linear equation, we have:

2A + 3B = 4.20

3A + 2B = 4.55

One way to solve this is to use elimination. We multiply the first equation by 3 and the second equation by 2.

6A + 9B = 12.60

6A + 4B = 9.10

Subtract the equations to cancel A.

5B = 3.50

Divide both sides of the equation by 5.

B = .70

So the cost of one banana is 70¢. We can substitute this value into one of the original equations to solve for the cost of an apple.

2A + 3(0.70) = 4.20

Simplify.

2A + 2.10 = 4.20

Subtract 2.10 from both sides.

2A = 2.10

Divide both sides by 2.

A = 1.05

So the cost of one apple is $1.05.