Problem of the Week July 26

Lower Elementary:

Question: Match the measurements on the left with the appropriate units of measure on the right:

Upper Elementary:

Question: Sammy is wrapping a birthday gift and wants to find out how much ribbon he’ll need. He wants to wrap the ribbon all the way around the gift box twice, then have an extra 1¹/₂ feet of ribbon for the bow on top. If the gift box is a cube that is 15 inches wide, how many inches of ribbon will he need?

Middle School:

Question: Ashley is playing a game on her smartphone that measures the distance she walks. Every 2 kilometers, the game gives her a prize. Ashley starts the game and then walks 5 miles. How many prizes does she earn?

(Hint: There are 1.609 kilometers in 1 mile.)

Algebra and Up:

Question: It takes Alice 45 minutes to complete a jigsaw puzzle. It takes Keisha an hour to complete a jigsaw puzzle of the same size. If they work together on the same jig­saw puzzle, how long will it take them to complete it?

ANSWERS ARE BELOW HERE!  

Lower Elementary:

Question: Match the measurements on the left with the appropriate units of measure on the right:

Answer:  The puppy can be measured in pounds, the football field can be measured in yards, the cookies can be measured in dozens, the Mathnasium sessions can be measured in hours, and the juice can be measured in cups.

Upper Elementary:

Question: Sammy is wrapping a birthday gift and wants to find out how much ribbon he’ll need. He wants to wrap the ribbon all the way around the gift box twice, then have an extra 1¹/₂ feet of ribbon for the bow on top. If the gift box is a cube that is 15 inches wide, how many inches of ribbon will he need?

Answer:  138 inches

Solution:  To go all the way around the box, the ribbon covers 15 inches, 4 times. That’s 60 inches. To wrap the ribbon all the way around the box twice, Sammy needs 60 × 2 = 120 inches of ribbon. For the bow, he’ll need an­other 1¹/₂ feet, or 18 inches. Altogeth­er, that’s 120 + 18 inches of ribbon.

Middle School:

Question: Ashley is playing a game on her smartphone that measures the distance she walks. Every 2 kilometers, the game gives her a prize. Ashley starts the game and then walks 5 miles. How many prizes does she earn?

(Hint: There are 1.609 kilometers in 1 mile.)

Answer:  4 prizes

Solution:  There are 1.609 kilometers to every mile. Ashley walks 1.609 kilome­ters, 5 times. That’s 8.045 kilome­ters. Since she’ll get a prize for every 2 kilometers she walks, she’ll earn 8 ÷ 2 = 4 prizes with 0.045 kilometers left over.

Algebra and Up:

Question: It takes Alice 45 minutes to complete a jigsaw puzzle. It takes Keisha an hour to complete a jigsaw puzzle of the same size. If they work together on the same jig­saw puzzle, how long will it take them to complete it?

Answer:  25⁵/₇ minutes

Solution:  Alice’s puzzle completing rate is 1 puzzle over 45 minutes, or ¹/₄₅. Kei­sha’s rate is ¹/₆₀. If we add them to­gether, we 1t, the rate at which they can solve 1 puzzle together.

¹/₄₅ + ¹/₆₀ = ¹/_t

To solve this, we need to multiply each side by the LCM of the denomi­nators, which is 180t. The result is:

4t + 3t = 180

t = 25⁵/₇