Math Problem Monday - December 5th, 2022 | Mathnasium Livermore, CA

Dec 5, 2022 | Livermore

Lower Elementary:
Question: At an arcade, Fiora earned 13 tickets. Cody earned twice as many tickets as Fiora. Manny earned twice as many as Cody. How many tickets did Manny earn?
Answer: 52 tickets
Solution: Cody earned twice as many tickets as Fiora and she earned 13 tickets. 13 doubled = 10 doubled + 3 doubled = 20 + 6 = 26. Cody earned 26 tickets. Manny earned twice as many tickets as Cody. 26 doubled = 20 doubled + 6 doubled = 40 + 12 = 52. Cody earned 52 tickets.

boxUpper Elementary:
Question: Penelope is packing her toys into boxes. She has 60 toys. She has 4 small boxes and 2 large boxes. She puts 8 toys into each of the small boxes. If she wants to divide them evenly, how many toys go in one large box?
Answer: 14 toys
Solution: First, let’s find how many toys are put in all of the small boxes. There are 8 toys per small box and there are 4 small boxes. 8 × 4 = 32. There are 32 total toys in all of the small boxes. She has 60 toys, so that means she has 60 – 32 = 28 toys to put in the large boxes. She has 2 large boxes, so that means that 28 ÷ 2 = 14 toys are put in each large box.

computerMiddle School:
Question: A computer program takes a number that the user inputs and then performs the following operation to it: n + (n – 5)2 × 3 where n is the number that was inputted. The answer is then displayed on screen. If a user enters the number 16 into the program, what number will display on screen?
Answer: 379
Solution: Because the user inputted the number 16, the program will compute 16 + (16 –5)2 × 3. Going in PEMDAS order, first we do what is in the parenthesis.
16 + (11)2 × 3
Next we compute the exponent.
16 + 121 × 3
Then we do multiplication and division.
16 + 363
Finally, we do the addition and subtraction.
The number that will display on screen 379.

snowmanAlgebra and Up:
Question: Paul is making a snowman. He rolls a big snowball for the body and a smaller snowball for the head. The radius of the body is 3 feet and the diameter of the head is 2 feet. What is the volume of snow that Paul used to make the snowman?
Answer: 37 1/3π cubic feet, or 112/3π cubic feet
Solution: The volume of a sphere is 4/3πr3 where r is the radius. The volume of the body is 4/3π(3)3 = 4/3π(27) = 36π cubic feet. The diameter of the head is 2 feet, which means the radius is 1 foot. So, the volume of the head is 4/3π(1)3 = 4/3π(1) = 4/3π cubic feet. That means that the total volume of the snowman is 36π + 4/3π = 37 1/3π = 112/3π cubic feet.