Lower Elementary
Question: Rachel and Kayla sold cookies at a bake sale. Kayla sold three times as many cookies as Rachel. If they sold a total of 24 cookies, how many cookies did each girl sell?
Answer: Rachel sold 6 cookies and Kayla sold 18
Note: Students can use the guess and check method.
Upper Elementary
Question: Bryan has one fourth as many DVDs as his friend Michael, who has three times as many DVDs as James. If Bryan has 9 DVDs. How many DVDs do they have altogether?
Answer: 57 DVDs
Note: If Bryan has 1/4 as many DVDs as Michael then Michael has (9 x 4) 36 DVDs. If this is 3 times as many DVDs as James then James has (36 / 3) 12 DVDs.
Altogether they have 9 + 36 + 12 = 57 DVDs.
Middle School
Question: Michael’s school offers the following 4 elective classes: Art, Music, Technology, and Yearbook. Michael can choose 2 classes. How many different combinations of classes can Michael take? (There are no restrictions on the classes he can take.)
Answer: 6 combinations
Note: One way to figure it out is to list the different combinations. Art – Music, Art – Technology, Art – Yearbook. It is important to note that Art – Music is the same as Music – Art so the next combinations would be Music – Technology and Music – Yearbook. The final combination would be Technology – Yearbook. This gives 6 combinations.
You could also note there are 3 pairings with the first course and there are 2 pairings with the second and 1 with the third. 3 + 2 + 1 = 6. This is a faster way to solve the problem when there are more than 4 choices.
Algebra and Up
Question: David deposits $600 into an account that earns 4% interest compounded annually. If David doesn’t make any additional withdrawals or deposits, how long will it take his money to double? (Round answer to the year.)
Answer: 18 years
*Students may use calculators and if necessary provide the formula for compounded interest.
P = principal amount (initial investment)
r = interest rate (written as a decimal)
n = number of times interest is compounded a year
t = number of years
A = amount after time t years
Notes: Although the compound interest formula could be used to check to see between which two years the money would double, a faster route would be to use the formula to solve for time. First identify the known and unknown variables. P = 600, r = .04, n = 1, t = unknown and A = 1200 (since the amount doubles). Then we plug the known values in the formula and solve for the unknown.
1200 = 600 (1 + .04/1)(1*t) (simplify)
1200 = 600(1+ .04)t (simplify)
1200 = 600(1.04)t (divide both sides by 600)
2 = 1.04t (take the log of both sides, in this case I have used the natural log)
ln 2 = ln (1.04t) (use property of logarithms to rewrite ln(1.04t) as t* ln 1.04)
ln 2 = t * ln 1.04 (divide both sides by ln1.04
ln 2/ln 1.04 = t
17.67 = t
So t = 18 years.
