Answers to Problems of the Week - September 6 to September 12

Rewards for Problems of the week:

5 stars for the correct answer at your level; 10 stars for the next level; 20 stars for 2+ levels up.

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.

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.

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.

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:  3â…“ gallons of recycled 20% mixture and 6â…” 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 = 3â…“. That means that there are 3â…“ gallons of recycled 20% mixture, so there must be 10 – 3â…“ = 6â…” gallons of recycled 50% mixture.

Challenge problem to take home. 5 stars for the correct answer. 

This trapezoid has an area of $$164$164$ square units. Its height is $$8$8$ units and the two non-parallel sides are $$10$10$ and $$17$17$ units.

What is the length of the shorter base in units?

Answer: 10 units