Click here [1] for the Problem Extension Worksheet version of the Problems of the Week.
Click here [2] for an MS Word version of the Problems of the Week.
Click here [3] for the Canadian Problem Extension Worksheet version of the Problems of the Week.
Click here [4] for a Canadian MS Word version of the Problems of the Week.
[5]Lower Elementary:
Question: Frankie buys a sandwich that costs $4.55 with a $5.00 bill, 2 quarters, and 1 dime. How much change does she get?
Answer: $1.05
Solution: Since 2 quarters are worth 50¢ and a dime is worth 10¢, Frankie pays for her sandwich with $5.00 + $0.50 + $0.10 = $5.60. So, she gets $5.60 – $4.55 = $1.05 in change.
[6]Upper Elementary:
Question: Emily is baking cookies. She arranges the cookie dough blobs on a baking sheet in 7 rows. Every even numbered row has 7 cookies, and every odd row has 8. How many cookies does Emily bake?
Answer: 53 cookies
Solution: The even rows—the 2nd, 4th, and 6th rows—each have 7 cookies. Three rows of 7 cookies have 7 × 3 = 21 cookies. The odd rows—the 1st, 3rd, 5th, and 7th rows—each have 8 cookies. Four rows of 8 cookies have 8 × 4 = 32 cookies. That makes 21 + 32 = 53 cookies in total.
[7]Middle School:
Question: Billy and Cody have a pizza-eating contest to see who can eat a whole pizza faster. Billy can eat a sixth of a pizza in 21/2 minutes. Cody can eat an eighth of a pizza in 11/2 minutes. By how many seconds does the pizza-eating contest winner win?
Answer: Cody wins by 180 seconds.
Solution: Billy finishes his pizza in 21/2 × 6 = 15 minutes. Cody finishes his pizza in 11/2 × 8 = 12 minutes. That means that Cody finishes the pizza 15 – 12 = 3 minutes faster, and 3 minutes is equal to 3 × 60 = 180 seconds.
[8]Algebra and Up:
Question: The volume of a cone is 1/3 × the area of its base × its height. Allison orders a cone-shaped hand roll from a sushi restaurant that is made of seaweed filled with rice, eel, and avocado. If the hand roll is 2 inches across at its base, its height is 2 inches, and a third of it is filled with eel and avocado, what is the volume of the rice inside the hand roll?
Answer: 4/9π inches cubed
Solution: The base of the cone has a diameter of 2 inches, which means its radius is 1 inch, so its area is πr2 = π. If we plug that value into the formula for the area of a cone, we get 1/3 × π × 2 = 2/3π inches cubed. Since a third of it is filled with eel and avocado, that means two thirds of it is filled with rice. Two thirds of 2/3π is 4/9π inches cubed.
2 Comments To "Problems of the Week – March 18 to March 22"
#1 Comment By Kip Fisher On March 17, 2019 @ 1:41 pm
I don’t get the Lower Elementary Problem. The $5 bill more than pays for the sandwich. Why would Frankie give the (unnecessary) coins to the cashier?
Possible answer: To get rid of the three coins in favor of a $1 bill and a single coin.
But the question still seems strange.
#2 Comment By Jane Adams On March 17, 2019 @ 1:56 pm
Hello, Kip!
Your theory is correct. In this problem, Frankie paid more than she needed to in order to receive a whole dollar and a single coin in change.