Answers to Problems of the Week - August 23 to August 29

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: A red-eyed tree frog has 4 toes on each front foot and 5 toes on each back foot. How many toes does a red-eyed tree frog have?

Answer:  18 toes

Solution:  The frog has 4 + 4 = 8 front toes and 5 + 5 = 10 back toes. That makes a total of 8 + 10 = 18 toes.

Upper Elementary:

Question: Luke says he saw a piranha that was 4¾ inches long. Howard says he saw a piranha that was 4.7 inches long. Who saw the bigger piranha?

Answer:  Luke

Solution:  One way to solve this problem is to write both measurements as decimals. Since ¼ is equal to 0.25, ¾ must be equal to 0.25 + 0.25 + 0.25 = 0.75. That means that a piranha that is 4¾ inches long is 4.75 inches long. Since 4.75 is greater than 4.7, Luke saw the bigger piranha.

Middle School:

Question: A kapok tree is 200 feet tall. A vine growing up the trunk of the tree overtakes 10% of the tree’s remaining height each week. How high does the vine reach after 3 weeks?

Answer:  54.2 feet

Solution:  On the first week, the vine grows 10% of 200 = 20 feet, leaving 200 – 20 = 180 feet untouched. On the second week, it grows 10% of 180 = 18 feet, leaving 162 feet untouched. On the third week, it grows 10% of 162 = 16.2 feet. So, in total, the vine has grown 20 + 18 + 16.2 = 54.2 feet up the tree.

 Algebra and Up:

Question: A biologist is monitoring a flock of toucans. The biologist determines that the number of toucans in the flock can be estimated using the function f(n) = 22 + 3n, wherein n is the number of toucan nests that the biologist counts in the flock’s territory. If the biologist counts 5 nests, what is the estimated number of toucans?

Answer:  37 toucans

Solution:  If the biologist counts 5 nests, then n = 5. So, f(5) = 22 + 3(5). That’s 22 + 15 = 37. That means that f(5) = 37 toucans.

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

In New Math City, streets follow a square grid with integer coordinates. The distance between any two points is the sum of their horizontal and vertical differences in units.

Children have to choose a school no farther than four blocks away from their home. There are two schools in the neighborhood — The Amazing School at (1,-2) and The Brilliant School at (-3,1).

Percy, Queenie, Raquel, and Sid live at (1,1), (0,-1), (-2,-1), and (-3, -1), respectively. How many of these four kids can choose between the two schools?

Answer: Two - Percy and Raquel