Answers to Problems of the Week - January 4 to January 9

Rewards for Problems of the week:

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

 Lower Elementary:

Question: Abby has $5.00 to spend on snacks. Cookies cost 50¢ per cookie, chips cost 75¢ per bag, and juice costs $1.00 per bottle. If Abby buys one of each, how much money will she have left?

Answer:  $2.75

Solution:  Abby’s snacks cost $0.50 + $0.75 + $1.00 = $2.25. So, Abby will have $5.00 – $2.25 = $2.75 left.

Upper Elementary:

Question: Brianna has a box that can hold up to 50 pounds. She puts 3 books that each weigh 2 pounds inside the box. She also puts a lamp that weighs 20 pounds inside the box. What percent of the box’s maximum weight capacity does Brianna have left to fill? 

Answer:  48%

Solution:  Brianna puts 3 × 2 + 20 = 26 pounds of stuff into the box. That means the box can hold another 50 – 26 = 24 pounds. Since 50 is half of 100 and percents are out of 100, we can double 24 to find that there is still 48% of the box’s maximum weight capacity left to fill.

 Middle School:

Question: Caleb has an aquarium that is 2 feet long, 1 foot wide, and 1 foot tall. A gallon is equal to 231 cubic inches. How many whole gallons of water can the aquarium hold?

Answer:  14 gallons

Solution:  The aquarium is 24 inches long, 12 inches wide, and 12 inches tall. So, its volume is 24 × 12 × 12 = 3,456 cubic inches. When we divide 3,456 by 231, we get 14 whole gallons and a remainder of 222 cubic inches.

Algebra and Up:

Question: Darcy is decorating her bedroom and sketches a floor plan to a 1:12 scale. What is the area of the surface of a desk that is 31/2 inches long and 21/4 inches wide on Darcy’s sketch? 

Answer:  77/8 square feet

Solution:  If the scale is 1:12, then 1 inch on the sketch represents 12 inches in the real world. So, an inch on the map is a foot in real life. The surface of the desk therefore has an area of 31/2 × 21/4 = 77/8 square feet.

Challenge problem to take home. 20 points for the correct answer. 

Preeti has a colorful, multi-patterned collection of socks. She has 12 pairs of socks, but each pair is different.

If Preeti grabs a pair of socks at random from her sock drawer, what is the probability she gets a matched pair?

Answer: 1/23