Math Problem Monday - October 11th, 2021 | Mathnasium Livermore, CA

Oct 11, 2021 | Livermore

Lower Elementary:
Question: The flowers in a park are arranged in a specific order around a circular fountain. The flowers are arranged a tulip, then a poppy, then a sunflower, then a lily, then a tulip, then a poppy, then a sunflower, then a lily, and the pattern continues all the way around the fountain. What will the 15th flower in the pattern be?
Answer: A sunflower
Solution: There are 4 flowers in the pattern: tulip, poppy, sunflower, lily. So, every 4 flowers the pattern repeats. The 4th flower is a lily, the 8th flower is a lily, and the 12th flower is a lily. This means that the 13th flower is a tulip, the 14th flower is a poppy, and the 15th flower is a sunflower.

pizzaUpper Elementary:
Question: Yumi is ordering food for delivery. She ordered 3 pizzas for $8 each, 2 salads for $6 each, a bottle of soda for $2, and she had to pay a $2 delivery charge. How much does Yumi have to pay for the food?
Answer: $40
Solution: If one pizza costs $8, then three pizzas cost $24. If one salad costs $6, then two salads cost $12. So, to find the total amount that Yumi owes, we add the total for each of the foods. $24 + $12 + $2 + $2 = $40. The food will cost $40.

moneyMiddle School:
Question: There are two possible investment plans that a bank offers for a two year investment. The first plan is to pay 10% interest both years. The second plan is to pay 15% interest the first year and 5% interest the second year. Which investment plan is better?
Answer: The first plan: 10% both years.
Solution: One way to solve this problem is to pick a value to begin the investment with and see how the interest accumulates. Since percent means for each hundred, let’s have the initial amount be $100. Under the first plan, 10% of 100 is 10. So, the amount after the first year is $100 + $10 = $110. For the second year, we need to find 10% of the new total. 10% of $110 is $11. So, the amount after the second year is $110 + $11 = $121. Now let’s see how much we can make with the second plan. Under the second plan, 15% of 100 is 15. So, the amount after the first year is $100 + $15 = $115. For the second year, we need to find 5% of 115. Since 5 is 1/20 of 100, one way to find 5% of 115 is to find 1/20 of 115. 1/20 of 115 is 5.75. So, the amount after the second year is $115 + $5.75 = $120.75. So for $100, the first plan makes 25¢ more interest, so it is the better plan.

diceAlgebra and Up:
Question: What is the probability of rolling 3 six-sided dice and getting a sum of 5?
Answer: 1/36
Solution: One way to solve this problem is to first find out the total number of outcomes. Since there are 6 outcomes for each die, the total number of outcomes is 6 × 6 × 6 = 216. Next, we need to find the total number of ways that we can get a sum of 5. The possible outcomes to get a sum of 5 are (1, 1, 3), (1, 3, 1), (3, 1, 1), (1, 2, 2), (2, 1, 2) and (2, 2, 1). So, there are 6 possible ways of getting a sum of 5. So, the probability of rolling a sum of 5 on three dice is 6/216 = 1/36.

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