Answers to Problems of the Week - July 26 to August 1

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: Crayons come in boxes of 12. Each crayon costs 10¢. How much does a box of crayons cost?

Answer:   $1.20

Solution:   Each crayon costs 10¢, so the whole box costs 10¢, 12 times. We can solve this by counting by 10s, or we can say that 10 × 12 = 120¢. Since 100¢ is the same as $1.00, 120¢ is the same as $1.20

Upper Elementary: 

Question: A pack of 3 glue sticks has enough glue in it to cover a square yard—that’s 9 square feet. How many glue sticks would you need to completely cover a banner that is 21 square feet in glue?

Answer:   7 glue sticks

Solution:   Because 3 glue sticks cover 9 square feet, 1 glue stick covers 9 ÷ 3 = 3 square feet. Inside of 21 square feet, we have 3 feet, 7 times because 21 ÷ 3 = 7. So, you need 7 glue sticks for the banner.

Middle School: 

Question: The sticker price of a calculator is $16.00. If you have a 15% off coupon and pay 10% sales tax, how much will the calculator cost you? 

Answer:   $14.96

Solution:   After the coupon is applied to the price of the calculator, it costs $16.00 × 0.85 = $13.60. Next, we add the sales tax; 10% of $13.60 is $1.36, and $13.60 + $1.36 = $14.96.

 Algebra and Up:

Question: The formula for the lateral surface area of a cone—that’s the surface that isn’t the base—is π × r × sqrt(h² + r²); h is the height of the cone and r is the radius of its base. A circular #2 pencil is 6 mm in diameter, and a pencil sharpener creates a cone-shaped end that is 20 mm in height. Find the surface area of the sharpened part of the pencil. Find the exact answer, then find an approximate answer.

Answer:   3π × sqrt(409), approximately 60π mm²

Solution:   First, we plug the radius of the base, which is half the diameter of the pencil or 3 mm, and the height of the sharpened part into the formula. We get π × 3 × sqrt(20² + 3²), or 3π × sqrt(409). This is our exact answer. We can approximate that the square root of 409 is about 20 because 20² = 400 and 21² = 441, and 409 is closer to 400. That gives us 3π × 20 = 60π mm², approximately.

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

In this Calcdoku puzzle,

• every row and every column contains every digit 1 through 4 exactly once, and
• every region completes its stated value.

Answer: There are multiple possible solutions to this puzzle, based on this: