Answers to Problems of the Week - December 7 to December 12

Rewards for Problems of the week:

5 points for the correct answer at your level; 10 points for the next level; 20 points each for 2+ levels up.

Lower Elementary:

Question: Ella plants a dozen seeds. Half of those seeds sprout and grow into plants. Each of those plants grows 3 flowers. How many flowers does Ella have?

Answer:  18 flowers

Solution:  A dozen means 12. So, since half of Ella’s 12 planted seeds sprout, that means 6 seeds sprout and grow into plants. Each of those plants grows 3 flowers, so Ella has 3 + 3 + 3 + 3 + 3 + 3 = 18 flowers.

Upper Elementary:

Question: A truck that weighs 4 tons when empty carries 1 ton of gravel. The driver unloads 500 pounds of gravel at a construction site. How many pounds do the truck and the gravel weigh in total now?

Answer:  9,500 pounds

Solution:  A ton is 2,000 pounds, so the truck itself weighs 2,000 × 4 = 8,000 pounds. The truck starts with 2,000 pounds of gravel, so after it leaves the construction site, it has 2,000 – 500 = 1,500 pounds of gravel in the back. In total, that’s 8,000 + 1,500 = 9,500 pounds.

Middle School:

Question: Mason scores 40 points on his fifth of five quizzes, increasing his average score to 32 points. What was Mason’s average score after the first four quizzes?

Answer:  30 points

Solution:  If Mason’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: Puppies sleep an average of 12 hours each day. Kittens sleep an average of 20 hours each day. If a puppy is 4 weeks older than a newborn kitten, then how old will the kitten be when the kitten and the puppy have gotten the same amount of sleep in total?

Answer:  42 days

Solution:  There are 28 days in 4 weeks, so the puppy has gotten 12 × 28 = 336 hours of sleep by the time the kitten is born. We want to know when the amount of sleep is equal. The kitten sleeps at a rate of 20 hours per day, and the puppy sleeps 12 per day with a 336-hour lead. We can set up the following equation and solve for d days:

20d = 12d + 336

d = 42

The kitten will be 42 days old.

Challenge problem to take home. 20 points for the correct answer. 

In this circle puzzle, dashed arrows denote addition, while solid arrows denote multiplication. If all the circles must contain different positive integers, which number will replace the question mark?

Answer: 3