Problem of the Week Sept 3

Here is this week’s Problem of the Week for our awesome mathletes!  

Make sure you revisit this page to get a new problem every week and to improve your problem solving skills for math.

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?

Upper Elementary:

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?

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?

Algebra and Up:

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)

WARNING:  ANSWERS COMING UP!!!!

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:

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.

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:

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.

Each of these problems is a stepping stone to algebra readiness, beginning with lower elememntary. Many people assume being algebra ready is the course preceding Algebra or Integrated Math. It isn't. It's the build up of all math that has been taught to date. It begins in kindergarden and progresses from there!

Staying on top of skills while in lower level courses sets the trajectory for math success! Students who notice a drop in grades and, more importantly, their understanding of concepts, are destined to be challenged in future courses.

These weekly problem solving opportunities are perfect for math enrichment, a math challenge, advanced problem solving for younger students, or good review for those who have completed algebra but want to refresh algebra skills in preparing for the SAT or ACT tests.