Answers to Problems of the Week - September 27 to October 3

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:  Emily was bringing balloons to a party, but a gust of wind blew 11 of them away. If she has 18 balloons left, how many balloons did she start with?

Answer:   29 balloons

Solution:   The 11 balloons that blew away were part of the whole number of balloons Emily had. She was left with 18 balloons, which is part of the whole number she started with. Since a whole = part + part we have, 11 + 18 = 29 balloons.

Upper Elementary: 

Question:  For lunch, Misha had a 590 calorie double cheeseburger, 595 calories of french fries, and a 440 calorie soda. If Misha can burn 650 calories per hour swimming at a vigorous pace, how long will it take Misha to burn off all her lunch calories?

Answer:   2 hours

Solution:    Find the total calories for Misha’s whole meal, 590 + 595 + 440 = 1,625 calories. Misha can burn 650 calories per hour swimming so we need to find how many 650s are inside of 1,625. 650 + 650 = 1300. Leaving 1,625 − 1,300 = 325 calories, which is half of 650.

So, 650 + 650 + 325 = 1 hr + 1 hr +  hr = 2 hours to burn off her lunch.

Middle School: 

Question:  Tej is building a brick wall. The entire wall will have 486 bricks. On the first day he lays 243 bricks but was more and more tired as the days went on. Each day after the first he only lays of the number

 Answer:   7 days

Solution:   First we find 486 − 243 = 243 bricks left to lay after the first day. Each of the following days he lays  of the amount left from the previous day.   of 243 = 162. He laid 162 bricks on day 2, leaving 243 − 162 = 81 bricks to be laid. If we repeat this process, at the end of day 6 he will only have 1 more brick to lay. Since, we can’t take a fraction, day 7 will be an easy one and Tej will only have to lay one brick.

Algebra and Up:

Question:  What is the area of Quadrilateral QRST, given QR = 12, RS = 4, ST = 3, and QT = 13?

Answer:    24 units²

Solution:   First label the side lengths of the figure then draw a dashed line from R to T. Now we have a nice right triangle, RST. The side lengths form the Pythagorean triple (3, 4, 5), so RT = 5. 

Now we can find the areas of the triangles, QRT = (12)(5) = 30 units² and RST =  (4)(3) = 6 units². Subtracting the area of triangle RST from QRT, 30 units² − 6 units² = 24 units².

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

 Hamza and Matthew are playing a game of Nim with a single pile of $$ 28  stones with these rules:

• They take turns removing 1, 2, or 3 stones from the pile.
• Whoever removes the last stone wins.

Assuming Hamza goes first and both players play perfectly, how many stones should Hamza remove on his first turn if he hopes to win? 

Answer: It's impossible for Hamza to win