Answers to Problems of the Week - August 2 to August 8

Rewards for Problems of the week:

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

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 = 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.

Challenge problem to take home. 5 stars for the correct answer. 

Ethan's first day as a waiter isn't going too well — he completely forgot which of the four guests ordered which of the four different plates he's carrying. If at least one guest receives the meal they wanted, Ethan won't get into serious trouble.

In how many ways can he bring at least one meal to the correct person?

Answer: 15 ways