Answers to Problems of the Week - November 16 to November 21

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:  Lauren has $1.00 in coins. She has 1 quarter, 3 dimes, and the rest are nickels. How many nickels does Lauren have?

Answer:  9 nickels

Solution:   Since a quarter is worth 25¢ and a dime is worth 10¢, Lauren has 25¢ + 10¢ + 10¢ + 10¢ = 55¢. Since she has $1.00 worth of coins, that means she has 100¢ – 55¢ = 45¢ in nickels. It takes 9 nickels to make 45¢. So, Lauren has 9 nickels.

Upper Elementary:

Question:  A local scout troop is hosting a fundraising talent show. They sold child tickets for $5.00 each and adult tickets for $10.00 each. They made $400.00. If they sold 12 adult tickets, how many child tickets did they sell?

Answer:  56 tickets

Solution:   The scout troop made $10.00 × 12 = $120.00. Since they made a total of $400.00, they made $400.00 – $120.00 = $280.00 from the sale of child tickets. Since they sold child tickets for $5.00 each, the number of child tickets they sold was $280.00 ÷ $5.00 = 56 tickets.

Middle School:

Question:  Three pounds of dog food is enough to feed 8 dogs for a day. Exactly how many pounds of dog food are needed for 18 dogs?

Answer:  63/4 pounds of food

Solution:   Since 3 pounds of dog food is enough to be divided among 8 dogs, each dog eats 3/8 of a pound of dog food. So, 18 dogs will need 3/8 × 18 = 54/8 = 63/4 pounds of food.

Algebra and Up:

Question:  James can paint a fence in 2 hours. Jessie 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:  James can paint 1 fence in 2 hours, so his rate is 1 fence/2 hours. Jessie can paint 1 fence in 3 hours, so her rate is 1 fence/3 hours. If we add their rates together, we get the rate at which they can paint a fence if they work together: 1 fence/2 hours + 1 fence/3 hours = 1 fence/x hours. If we solve for x, we get x = 6/5 = 11/5. So, James and Jessie can paint a fence together in 11/5 hours, or 1 hour and 12 minutes.

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

The top scale is in balance.

On which side should you place the square to balance the bottom scale?

Answer: Left