Problems of the Week Jan 15 to Jan 19

Jan 13, 2018 | Cambridge

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.

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