Math Problems of the Week - Aug. 27, 2023 to Sept. 2, 2023

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 32x5=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 12x28=336 hours of sleep by the time of 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.