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Problems of the Week – July 9 to July 13

Click right here [1] for the Problem Extension Worksheet version of the Problems of the Week.
Click here [2] for an MS Word version of the Problems of the Week.
Click over here [3] for the Canadian Problem Extension Worksheet version of the Problems of the Week.
Click here [4] for a Canadian MS Word version of the Problems of the Week.

[5]Lower Elementary:
Question: Charlotte and Chuck have tickets to a movie that starts at 7:30 PM. If it’s 6:42 PM now, then how much time do Charlotte and Chuck have to get to the movie theater before the show starts?
Answer: 48 minutes
Solution: We can solve this problem by adding the minutes up to 7:30 PM. There are 18 minutes until 7:00 because 42 + 18 = 60 minutes, which is an hour. There are 30 minutes from 7:00 until 7:30. So, Charlotte and Chuck have 18 + 30 = 48 minutes until the movie starts.

[6]Upper Elementary:
Question: Dillon wants to buy a model airplane that costs $34.00. She has a $5.00 bill and a 75% off coupon. How much more money does Dillon need to get the model airplane?
Answer: $3.50
Solution: Since the coupon is for 75% off, the model airplane costs 25% of its original cost, which is half of a half of $34.00. Half of $34.00 is $17.00, and half of that is $8.50. If Dillon has $5.00, she needs $8.50 – $5.00 = $3.50 more to buy the model airplane.

[7]Middle School:
Question: For the first 5 days of the week, Eddie put 3 photos on social media per day. How many does he need to post on the weekend to have an average of 5 photos posted per day for the whole week?
Answer: 20 more photos
Solution: If Eddie posts 3 photos per day for 5 days, then he posts 3 × 5 = 15 photos. In order for Eddie’s average to be 5 photos per day for a week, he’ll need to post a total of 5 × 7 = 35 photos. So, he needs to post 35 – 15 = 20 more photos over the weekend to bring his average to 5 photos per day.

[8]Algebra and Up:
Question: A hardware store receives an order for 10 gallons of paint with 40% blue pigment. The hardware store already has mixtures of 20% blue pigment and 50% blue pigment. How many gallons of each can the hardware store reuse to mix 10 gallons of 40% blue pigment?
Answer: 3⅓ gallons of recycled 20% mixture and 6⅔ gallons of recycled 50% mixture
Solution: 40% of 10 gallons of paint is 4 gallons, so we know that the total amount of pigment in the mixture must be 4 gallons. We can set up an equation to solve for x, the amount of recycled 20% mixture in the new paint mixture:

0.20x + 0.50(10 – x) = 4

Notice that the amount of recycled 50% mixture is 10 – x. This is because every part of the 10 gallons of paint that isn’t the recycled 20% mixture is the 50% mixture. When we solve for x, we find that x = 3⅓. That means that there are 3⅓ gallons of recycled 20% mixture, so there must be 10 – 3⅓ = 6⅔ gallons of recycled 50% mixture.