Problems of the Week – September 3rd to September 7th

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.

Lower Elementary:
Question: A bakery is having a half-price sale on donuts. A half-dozen donuts are only $3.00! How much do a dozen donuts cost at their regular price?
Answer:  $12.00
Solution:   If something is on sale for half price, the sale price is half of the regular price. Since a half-dozen donuts cost $3.00 on sale, we can double $3.00 to find the regular price. $3.00  doubled is $6.00.
Two half-dozens equal one dozen. Since a half-dozen donuts cost $6.00 at regular price, a dozen donuts cost $6.00 + $6.00 = $12.00 at regular price.

Upper Elementary: ^[5]

Question: Eric has $31.00 to spend on groceries. He has 4 boxes of cookies that cost $2.85 each and a half-gallon of milk that costs $3.50 in his cart already. How much money does Eric have left to spend on his other groceries?
Answer:  $16.10
Solution:  The 4 boxes of cookies cost 4 × $2.85 = $11.40. The cookies plus the milk cost $11.40 + $3.50 = $14.90. Subtracting $14.90 from $31.00, we get $16.10.

^[6]Middle School:
Question: Russell’s new diesel car gets 41 miles per gallon. He wants to take a road trip from Los Angeles to Dallas, a distance of 1,435 miles. The average price of diesel for the whole trip is $3.73 per gallon. How much will the fuel cost for the whole trip, there and back?
Answer:  $261.10
Solution:  The round trip is 1,435 × 2 = 2,870 miles. Russell’s car gets 41 miles per gallon, so he needs 2,870 miles ÷ 41 mpg = 70 gallons of fuel for the whole trip. The average price of diesel is $3.73 per gallon. The cost for fuel for the whole trip is $3.73 × 70 = $261.10.

Algebra and Up: ^[7]
Question: Shiv has two fish tanks. One is shaped like a rectangular prism that measures 25 inches long by 10 inches wide by 15 inches high. The other tank is shaped like a cylinder with a 10-inch radius and a 12-inch height. Which tank can hold the most water? How much more water can it hold than the other tank? (Round π to 3.14)
Answer:  The cylindrical tank hold 18 in³. more water than the rectangular prism.
Solution:  The volume of the rectangular prism tank is 25 in × 10 in × 15 in = 3,750 in³.
The volume of the cylindrical tank is  (3.14)(10)2(12) ≈ 3,768 in³.
The cylindrical tank holds 3,768 − 3,750 = 18 in³ more water than the rectangular prism tank.