Answers to Problems of the Week - January 25 to January 30

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: Willy bought a candy bar for 99¢ and a bottle of water for $1.26. If he pays with a $5 bill, what is Willy’s change?

Answer:  $2.75

Solution:  The total amount Willy spent is 99¢ + $1.26 = $2.25. Because he pays $5, he will receive $5.00 – $2.25 = $2.75 as change.

Upper Elementary:

Question: Tiffany arrived at the airport at 3:50PM. Her flight was supposed to leave at 5:15PM, but it was delayed for 2 hours. How long was Tiffany at the airport before her flight left?

Answer:  3 hours and 25 minutes

Solution:  The plane left 2 hours after 5:15PM, which means it left at 7:15PM. It is 25 minutes from 3:50PM to 4:15PM and then it is 3 hours from 4:15PM to 7:15PM, so the total time Tiffany was at the airport was 3 hours and 25 minutes.

Middle School:

Question: There are three candidates for class president. Becky received 25% of the total votes. Charles received 45% of the votes. Daniella received 300 votes. What is the total number of votes in the election?

Answer:  1,000 votes

Solution:  We need to find the percent of the votes that Daniella received. From 100% of the votes, Becky has 25% of the votes and Charles has 45% of the votes. So Daniella has 100% – 25% – 45% = 30% of the votes. Since 300 votes represent 30% of the total votes, that means that 100 votes represent 10% of the total votes. So 1,000 votes represent 100% of the total votes.

Algebra and Up:

Question: Gerald can paint a fence in 2 hours. Mandy can paint a fence in 3 hours. How long will it take them to paint a fence together?

Answer:  1 hour and 12 minutes

Solution:  Gerald can paint 1 fence in 2 hours, so his rate is 1/2. Mandy can paint 1 fence in 3 hours, so her rate is 1/3. If we let x be the rate at which they can paint a fence together, they can paint 1 fence in x hours, so the rate is 1/x. So our equation is:

1/2  + 1/3 = 1/x

Combine the fractions.

5/6 = 1/x

Find the cross product.

5x = 6

Divide by 5.

x = 6/5  = 1 1/5

Together, Gerald and Mandy can paint a fence in 1 and 1/5 hours, or 1 hour and 12 minutes.

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

What is the sum of all six colored angles?

Answer: 360^o