Problems of the Week 2/6/2017

Lower Elementary:
Question: Wyatt has 20 stickers. He wants to give 6 to his friend Henry, 7 to his friend Ellie, and 8 to his friend Noah. How many stickers will Wyatt have left over?
Answer: Wyatt can’t give that many stickers to his friends.
Solution: Wyatt has 20 stickers. If he gives away 6, he will have 20 – 6 = 14 left. If he gives away 7 of those, he’ll have 14 – 7 = 7 left. If Wyatt only has 7 stickers left to give to Noah, then it’s impossible for him to give Noah 8 stickers.

Upper Elementary:
Question: Christian has two-thirds of a pound of chocolate chips. Kaylee has 0.25 pounds of chocolate chips. How much more do they need to have a whole pound of chocolate chips?
Answer: 0.0833… pounds or one-twelfth of a pound
Solution: We need to either convert the fraction to a decimal or the decimal to a fraction: two-thirds = 0. 666…, and 0.25 = one-fourth. Two-thirds + one-fourth = eleven-twelfths, so they would need one-twelfth of a pound more. 0.666… + 0.25 = 0.916…, so they would need 0.083… pounds more.

Middle School:
Question: Gabriel scores 40 points on his fifth of five quizzes, increasing his average score to 32 points. What was Gabriel’s average score after the first four quizzes?
Answer: 30 points
Solution: If Gabriel’s average point score over 5 tests was 32 points, then he must have earned 32 × 5 = 160 points in total. Before his last test, he had 160 – 40 = 120 points over 4 tests. So, his average score after 4 tests was 120 ÷ 4 = 30 points.

Algebra and Up:
Question: Matthew bets Nora a pepperoni pizza that if he rolls a pair of six-sided dice, the resulting sum will be a prime number. Nora takes the bet. What are the odds that Nora will win?
Answer: 7 out of 12
Solution: The prime numbers that are possible are 2, 3, 5, 7, and 11. There is 1 way to roll a 2 (1 + 1). There are 2 ways to roll a 3 (1 + 2 and 2 + 1). There are 4 ways to roll a 5 (1 + 4, 2 + 3, 3 + 2, and 4 + 1). There are 6 ways to roll a 7 (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, and 6 + 1). There are 2 ways to roll an 11 (5 + 6 and 6 + 5). So, there are 1 + 2 + 4 + 6 + 2 = 15 ways to roll a prime number with a pair of dice. There are 6 × 6 = 36 possible outcomes in total, so the probability of rolling a prime number is 5 out of 12. That means that the probability that Matthew will win is 5 out of 12, and the probability that Nora will win is 12 – 5 = 7 out of 12.