Math Problems of the Week - Sept. 25, 2022 to Oct. 1, 2022

Lower Elementary:

Question: An alligator starts life with 80 teeth. When an alligator tooth wears down or falls out, the alligator grows a new one. How many teeth has an alligator had in total if it has replaced each of its teeth 3 times?

Answer: 320 teeth

Solution: If the alligator regrows all 80 teeth, 3 times, then it regrows 80 + 80 + 80 or 80 x 3 = 240 teeth. When we add in the 80 teeth it started with, that makes 240 + 80 = 320 teeth.

Upper Elementary:

Question: A frog croaks 1 time when a storm is 1 mile (5,280 feet) away. When the storm is half of a mile away, the frog croaks 2 times. When the storm is a third of a mile away, the frog croaks 3 times. How many feet away is the storm when the frog croaks 5 times?

Answer: 1,056 feet

Solution: If the pattern continues, then the frog will croak 4 times when the storm is a fourth of a mile away and 5 times when the storm is a fifth of a mile away. Since a mile is 5,280 feet, one fifth of a mile is 5,280 ÷ 5 = 1,056 feet.

Middle School:

Question: Three loaves of stale bread is enough to feed 8 adult ducks or 16 ducklings. How many loaves of bread are needed to feed 6 adult ducks and 12 ducklings?

Answer: 4½ loaves of bread

Solution: Three loaves of bread can be divided among 8 ducks, so each duck gets 3 ÷ 8 = 3/8 of a loaf of bread. Because 16 ducklings eat the same amount of bread as 8 ducks, each duckling must eat half as much as an adult. So, 12 ducklings eat the same amount as 6 adults. That means that 6 ducks + 12 ducklings eat the same amount as 6 ducks + 6 ducks = 12 ducks. Twelve ducks eat 12 × 3/8 = 41/2 loaves of bread.

Algebra and Up:

Question: A heron is fishing in a pond that has 3 carp, 4 bass, and 5 trout. The heron catches the fish at random and swallows every fish it catches. What is the probability that the heron will catch a carp and then a trout?

Answer: 5 out of 44

Solution: To find the probability of the heron catching each fish, we divide the number of that species of fish by the total number of fish. So, there is a 3 ÷ 12 = 1/4 probability of catching a carp first. After the heron eats the carp, there are 11 fish left, so the probability of catching a trout next is 5 ÷ 11 = 5/11. The probability of catching a carp and then a trout is 1/4 × 5/11 = 5/44, or 5 out of 44.