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Problem of the Week 05-30-2017

May 30, 2017

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 4/3πr3, or 2/3πr3 (we can do this because half of 4/3 is 2/3). The volume of the cone is πr2h/3. We know that h = 5 and r = 1.5, so altogether, the volume of the snowcone is:

(2/3 × π × 1.53) +  (π × 1.52 × 5/3)

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