Lower Elementary:
Question: Rick wants to save water by shortening his shower to 5 minutes. To do this, he will play two songs that he knows will be 5 minutes when played together. He has four songs to choose from. Song One is 2 minutes and 25 seconds. Song Two is 3 minutes and 35 seconds. Song Three is 1 minute and 25 seconds. Song Four is 2 minutes and 15 seconds. Which two songs should Rick play so that he knows he took a 5-minute shower?
Answer: Song Two and Song Three
Solution: We need to find 2 songs that combined will be 5 minutes. Song Two is 3 minutes and 35 seconds and Song Three is 1 minute and 25 seconds. 3 minutes and 35 seconds + 1 minute and 25 seconds = 4 minutes and 60 seconds, which is the same as 5 minutes since 60 seconds = 1 minute. So Song Two and Song Three will be 5 minutes.
Upper Elementary:
Question: A jar contains 180 cheese puffs. Mark eats 8 cheese puffs a day and Tori eats 7 cheese puffs a day. How many days can Mark and Tori eat cheese puffs before the jar is empty?
Answer: 12 days
Solution: Mark eats 8 cheese puffs a day and Tori eats 7 cheese puffs a day. Altogether, they eat 15 cheese puffs. To see how many days they can eat the cheese puffs before the jar is empty, we take the total number of cheese puffs and divide by the number they eat per day. 180 ÷ 15 = 12. Mark and Tori can eat cheese puffs for 12 days before the jar is empty.
Middle School:
Question: Carlos ran the first 1.6 miles of his run in 15 minutes. His entire run took 25 minutes. If he ran at a constant speed, how much further did he run?
Answer: 1 1/15 miles
Solution: One way to solve this problem is to set up a proportion to see how long the entire run was. Let x be the total distance of the run. Setting up the proportion we have:
1.6 miles / 15 minutes = x miles / 25 miles
Cross multiply.
(1.6)(25) = 15x
Simplify the expression.
40 = 15x
Divide both sides be 15.
2 2/3 = x
The entire run is 2 2/3 miles. Carlos already ran 1.6 miles = 1 3/5 miles, so that means ran 2 2/3 – 1 3/5 = 1 1/15 miles after the first 15 minutes.
Algebra and Up:
Question: Thank you cards cost $2 per card. Birthday cards cost $3 per card. If Alex bought 20 cards and spent $47, how much of each card did Alex buy?
Answer: 13 thank you cards and 7 birthday cards
Solution: Let T represent the number of thank you cards and B represent the number of birthday cards. We can use the information to set up two equations: one for the number of cards and one for the cost of the cards.
2T + 3B = 47
T + B = 20
Multiply the second equation by –2.
2T + 3B = 47
–2T – 2B = –40
Add the equations together.
B = 7
So Alex bought 7 birthday cards. Since there is a total of 20 cards, Alex bought 20 – 7 = 13 thank you cards.
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