Lower Elementary
Question: Lilli has a black pair of shorts, a blue pair of shorts, a white shirt, a red shirt, and a yellow shirt. How many different outfits can she make?
Answer: 6 outfits
Note: There are several methods for solving this problem. Creating a tree diagram is helpful for visualizing the possible combinations.
Upper Elementary
Question: A spinner is divided into 12 equal sections. 2 of the sections are red, 5 sections are purple, 4 sections are blue, and 1 section is yellow. If you spin the spinner once, what is the probability that you will land on a section that isnot yellow or blue?
Answer: 7/12
Note: There are a total of 7 sections (2 red and 5 purple) that are neither yellow nor blue.
Middle School
Question: Gym A has a new membership fee of $15 and a monthly fee of $35. Gym B has an new membership fee of $60 and a monthly fee of $25. After how many months would a membership at Gym B be a better deal than Gym A?
Answer: After 4 months. During the 5th month, the total amount of money spent on membership at Gym A is greater than the total amount of money spent at Gym B.
Note: During the first month the new membership fee and the monthly fee are paid. Gym membership is paid at the beginning of each month.
An arithmetic solution: One method for solving this problem is to make a table that keeps track of how much total money is spent on each gym membership and find out when Gym B is less than Gym A.
Gym A: Month 1: (15 + 35) $50; Month 2: (50 + 35) $85; Month 3: $120; Month 4: $155; Month 5: $190
Gym B: Month 1: (60 + 25) $85; Month 2: (85 + 25) $110; Month 3: $135; Month 4: $160; Month 5: $185
An algebraic solution: We are looking for when the total cost of membership at Gym A is greater than the total cost of gym membership at Gym B. If we let m = number of months of gym membership, then the total cost for gym membership at Gym A = 35m + 15. The total cost of gym membership at Gym B = 25m + 60.
Then we solve the inequality: total cost Gym A > total cost Gym B
35m + 15 > 25m + 60
10m > 45
> 4.5 (means after 4 months since gym membership is paid at the beginning of each month.)
Algebra and Up
Question: Let the symbol # be defined as x # y = xy + xy , and x and y are positive integers. What is (1 # 3) # 6?
Answer: 4120
Note: Using order of operations: (1 # 3) # 6
= (13 + 1*3) # 6
= 4 # 6
= 46 + 4*6
= 4120
