# Math Problem Monday - December 19th, 2022 | Mathnasium Livermore, CA

Dec 19, 2022 | Livermore

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?
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.