Lower Elementary:
Question: Rui spends 8 quarters on drinks. She spends 2 quarters on a glass of apple juice and she spends the rest on cartons of orange juice that costs 1 quarter each. How many drinks does Rui buy altogether?
Answer: 7 drinks
Solution: Rui spends 2 quarters on one glass of apple juice. 8 –2 =6, so she has 6 quarters left. She spends the rest on orange juice cartons that are 1 quarter each. So, she buys 6 cartons of orange juice. Rui buys a total of 7 drinks (1 + 6).
Upper Elementary:
Question: Gilbert is buying a suit and tie. Suits cost $120 for 3 and ties cost $24 for 2. How much does Gilbert spend if she buys one suit and tie?
Answer: $52
Solution: Find the price for one suit and one tie. One suit is $40 (120 ÷ 3) and one tie costs $12 (24 ÷ 2). The total for one suit and tie is $40 + $12 = $52.
Middle School:
Question: Laurie is trying to solve a puzzle. The puzzle gives a phrase and each letter represents a number. A = –1, C = 5, I = 3, L = 2, P = 4, T = –2, and U = 1/2. A space represents a plus sign. Letters next to each other are multiplied. If Laurie is given the phrase “CLAP IT UP”, what is the solution to the puzzle?
Answer: –44
Solution: Letters next to each other are multiplied and then each of the words are added together. By the order of operations, we do multiplication first, and then addition. So let’s first figure out the number each word is.
CLAP = C × L × A × P = 5 × 2 × –1 × 4 = –40
IT = I × T = 3 × –2 = –6
UP = U × P = 1/2 × 4 = 2
Now we add each of the values together. –40 + –6 + 2 = –44. The solution to the puzzle is –44.
Algebra and Up:
Question: Andy has a collection of 60 CDs. Half of his CDs are hip hop, 12 are pop, and the rest are rock and roll. If he randomly selected one CD, what is the probability that the CD is a hip hop or a rock and roll CD?
Answer: 4/5
Solution: Fractional parts solution:
Find the fractional part of the collection that is rock and roll CDs. Hip hop is half of the collection. Pop is 1/5 of the collection (12/60 = 1/5). To find the fractional part of rock and roll, take the whole and subtract the sum of the other parts. 1 – 1/2 – 1/5 = 10/10 – 5/10 – 2/10 = 3/10. The fractional part is the same as the probability of drawing the CD. So, there is a 3/10 probability of picking a rock and roll CD. Since half of the CDs are hip hop, then there is a 1/2 probability of drawing a hip hop CD. Add the two probabilities together to get the probability of drawing a hip hop or a rock and roll CD.
3/10 + 1/2 = 3/10 + 5/10 = 8/10 = 4/5 probability.
Probability solution:
Half of 60 is 30, so there are 30 hip hop CDs. To find the total number of rock and roll CDs, take the total and subtract the other parts. 60 – 30 – 12 = 18. There are 18 rock and roll CDs. Probability is the total number of things you want over the total number of things to choose from. The probability of drawing a hip hop or a rock and roll CD is 48/60 = 4/5.
