Math Problem Monday - December 7th, 2020 | Mathnasium Livermore, CA

Lower Elementary:
Question: Megan bought 5 pieces of gum for 25¢ each and 2 pencils for 50¢ each. How much did Megan spend on gum and pencils altogether?
Answer: $2.25
Solution: First, let’s find the total amount Megan spent on gum. Each piece of gum costs 25¢, so to find out how many 5 pieces of gum cost, count by 25, 5 times. 25, 50, 75, 100, 125. 5 pieces of gum cost $1.25. Now, let’s find the cost of the pencils. One pencil costs 50¢, so 2 pencils costs $1.00. Add the amounts together to find the cost of the pieces of gum and the pencils. $1.25 + $1.00 = $2.25. Altogether, Megan spent $2.25 on gum and pencils.

Upper Elementary:
Question: Jordan started playing a new trading card game. He bought 2 starter box sets that come with 50 cards each. He then bought 12 packs that had 9 cards each. He then went to a trading card store where he traded away 3 of his cards to get 1 rare card. How many total cards does Jordan have altogether?
Answer: 206 cards
Solution: Jordan bought 2 starter box sets with 50 cards each. From the starter box set he received a total of 100 cards (2 × 50 = 100). He then bought 12 packs with 9 cards each. So from the packs he received a total of 108 cards (12 × 9 = 108). If we add these 2 totals together, Jordan has a total of 208 cards. He trades away 3 of them, so now he has 205 cards. He traded those 3 to receive another card, so altogether he has 206 cards total.

Middle School:
Question: Alvin can swim 510 meters in 5 minutes. How fast can Alvin swim in kilometers per hour?
Answer: 6.12 km/hr
Solution: One way to solve this problem is to convert the meters to kilometers, the minutes to hours, and then find the rate with the new units. There are 1,000 meters in 1 kilometer, so to convert from meters to kilometers, divide by 1,000. 510 ÷ 1,000 = 0.51 kilometers. There are 60 minutes in an hour, so to convert from minutes to hours, divide by 60. 5 ÷ 60 = 1/12 hour. Now, let’s divide the units. 0.51 km ÷ (1/12 hr). When we divide by a fraction, we multiply by the reciprocal. So we have 0.51 × 12 = 6.12. Alvin can swim at a rate of 6.12 km/hr.

Algebra and Up:
Question: 7 friends are in the theater watching a movie. They find a row that has 7 seats together but 2 of the friends are claustrophobic and need to sit at the ends of the row. How many different ways are there for the friends to sit in the row?
Answer: 240 ways
Solution: Let’s start with the first seat. The first seat has to be one of the 2 friends who are claustrophobic, so there are only 2 possible people to sit in the first seat. The second seat can be any of the 5 other friends, so there are 5 possible people to sit in the second seat. After someone sits in the second seat, there are now four friends to choose from for the third seat. So there are 4 possible people to sit in the third seat. Using this pattern, we have that there are 3 possible people to sit in the fourth seat, 2 possible people to sit in the fifth seat, and 1 possible person to sit in the sixth seat. The other claustrophobic friend must sit in the seventh seat, so there is 1 possible person to sit in the seventh seat. Now that we know how many possible people can sit in each seat, we multiply all of the numbers together to find the total number of ways the friends can sit in the row. 2 × 5 × 4 × 3 × 2 × 1 × 1 = 240. There are 240 different ways for the friends to sit in the row.