Mar 2, 2020 | High Park

Four more problems for you to solve this week, Mathletes! Good luck!

**Lower Elementary:**

*Question: *A clown makes 11 balloon poodles, 15 balloon octopuses, 4 balloon flowers, and a balloon giraffe. How many balloon animals does the clown make?

**Upper Elementary:**

*Question: *A spinning prize wheel has four different varieties of prizes. 40% of the prizes are items from a prize case. 30% of the prizes are tickets to a concert. 20% of the prizes are cash. The other 2 prizes are all-expense-paid trips. How many total prizes are on the wheel?

**Middle School:**

*Question: *A dunk tank is ^{4}/_{5} full. After Dave gets dunked, ^{1}/_{4} of the water splashes out. After that, there are 450 gallons of water left. How many gallons of water does the dunk tank hold when it’s full?

*Answer: *750 gallons

**Algebra and Up:**

*Question: *The paper cone of a snowcone is 5 inches deep and 3 inches wide at its opening. If the cone is filled to the top with snow and then a perfect hemisphere of snow is placed on top, what is the volume of the snow in cubic inches?

...

**Answers:**

**Lower Elementary:**

*Question: *A clown makes 11 balloon poodles, 15 balloon octopuses, 4 balloon flowers, and a balloon giraffe. How many balloon animals does the clown make?

*Answer: *27 balloon animals

*Solution: *The clown makes three different kinds of animals—poodles, octopuses, and giraffes. Let’s add them together, one species at a time. There are 11 poodles and 15 octopuses, and 11 + 15= 26. One more, the giraffe, makes 27.

**Upper Elementary:**

*Question: *A spinning prize wheel has four different varieties of prizes. 40% of the prizes are items from a prize case. 30% of the prizes are tickets to a concert. 20% of the prizes are cash. The other 2 prizes are all-expense-paid trips. How many total prizes are on the wheel?

*Answer: *20 prizes

*Solution: *First we need to know what percentage of the prizes are all-expense-paid trips. The rest of the prizes add up to 40% + 30% + 20% = 90%, so the other 10% of the prizes are all-expense-paid trips. If 2 is 10%, or one tenth, of the total, then there are 2 × 10 = 20 prizes on the wheel.

**Middle School:**

*Question: *A dunk tank is ^{4}/_{5} full. After Dave gets dunked, ^{1}/_{4} of the water splashes out. After that, there are 450 gallons of water left. How many gallons of water does the dunk tank hold when it’s full?

*Answer: *750 gallons

*Solution: *If ^{1}/_{4} of the water in a ^{4}/_{5}–full tank leaks out, then the tank is now ^{3}/_{5} full. If 450 gallons makes up ^{3}/_{5} of the tank’s capacity, then ^{1}/_{5} of it must be 450 ÷ 3 = 150 gallons. 150 gallons, 5 times makes ^{5}/_{5} of the tank’s capacity, and 150 × 5 = 750 gallons.

**Algebra and Up:**

*Question: *The paper cone of a snowcone is 5 inches deep and 3 inches wide at its opening. If the cone is filled to the top with snow and then a perfect hemisphere of snow is placed on top, what is the volume of the snow in cubic inches?

*Answer: *6π cubic inches

*Solution: *The volume of the semisphere of snow is equal to half of ^{4}/_{3}πr3, or ^{2}/_{3}πr3 (we can do this because half of ^{4}/_{3} is ^{2}/_{3}). The volume of the cone is πr2^{h}/_{3}. We know that h = 5 and r = 1.5, so altogether, the volume of the snowcone is:

Altogether, the above equals 2.25π + 3.75π = 6π cubic inches, or approximately 18.85 cubic inches.