Math Problem Monday - October 25th, 2021 | Mathnasium Livermore, CA

Oct 25, 2021 | Livermore

Lower Elementary:
Question: While Trick-or-Treating on Halloween, Henry got twice as much candy as Carly. Carly got twice as much candy as Becky. If Becky got 14 pieces of candy, how much candy did Henry get?
Answer: 56 pieces of candy
Solution: Carly got twice as much candy as Becky. 14 doubled = 10 doubled + 4 doubled = 20 + 8 = 28. Carly got 28 pieces of candy. Henry got twice as much candy as Henry. 28 doubled = 20 doubled + 8 doubled = 40 + 16 = 56. Henry got 56 pieces of candy.

bowl of candyUpper Elementary:
Question: Thomas bought value packs of candy to hand out to Trick-or-Treaters. Each bag has 6 different kinds of candy and there are 15 pieces of each kind. If Thomas buys 10 bags, how many total pieces of candy does he have?
Answer: 900 pieces of candy
Solution: One way to solve this problem is to find the total number of candies in a bag. Each bag contains 6 kids of candy and there are 15 of each kind of candy. 6 × 15 = 90. There are 90 pieces of candy per bag. Thomas buys 10 bags, so the total number of pieces of candy that Thomas has is 90 × 10 = 900 pieces of candy.

jellybeansMiddle School:
Question: Valerie and her friends went Trick-or-Treating in their neighborhood. They walked 2 miles up the street, then turned right at a corner and walked 1 and a half miles. To get home they cut through a park, and walked a straight direct path home. How many total miles did Valerie and her friends walk?
Answer: 6 miles
pathSolution: The shape that Valerie and her friends walked is a right triangle. We can use the Pythagorean Theorem to find the length of the path home. If we let a and b be the length that they walked, then the Pythagorean Theorem becomes:
22 + 1.52 = c2
Simplify the left side of the equation.
4 + 2.25 = c2
6.25 = c2
Take the square root of both sides.
2.5 = c
Valerie and her friends walked 2.5 miles home. The total distance they walked is the perimeter of the triangle. To find the perimeter, we add the lengths of all the sides. 2 + 1.5 + 2.5 = 6. They walked a total of 6 miles.

chocolateAlgebra and Up:
Question: Half of the candies in Joe’s candy bag are chocolates, one third of the candies are gummies, and the remaining candies are gumballs. If he draws one candy at random from the bag, what is the probability that the candy is a chocolate or a gumball?
Answer: 2/3
Solution: To solve this problem, we need to find the fractional part that the gumballs represent. Chocolates are 1/2 of the candies and gummies are 1/3 of the candies. To find the fractional part that is gumballs, take 1 and subtract the sum of the other parts. 1 – 1/2 – 1/3 = 1 – 3/6 – 2/6 = 1 – 5/6 = 1/6. The gumballs represent 1/6 of the candy. To find the probability of drawing a gumball or a chocolate, we add the fractional parts for each type of candy. 1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3. There is a 2/3 probability of drawing a chocolate or a gumball.

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