Answers to Problems of the Week - April 12 to April 17

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: Oscar sketched twice as many portraits as Polly. Polly sketched twice as many portraits as Kate. Kate sketched 4 portraits. How many portraits did Oscar sketch?

Answer:  16 portraits

Solution:  If Polly sketched twice as many as Kate, then she sketched 4 + 4 = 8 portraits. Oscar sketched twice as many as that, so he sketched 8 + 8 = 16 portraits.          

 Upper Elementary:

Question: Carlo had four 16–pound tubs of clay. After he sculpted a 36–pound bust, how many tubs of clay did he have left?

Answer:  1³/₄ tubs

Solution:  We can find out how many tubs Carlo used by dividing the amount of clay he used by the amount of clay per tub. That’s 36 ÷ 16 = 2 R4. Next, we can find out what fractional part of a tub got used by dividing the remainder by 16 again. That’s 4 ÷ 16 = ¹/₄. So, Carlo used 2¹/₄ tubs of clay. Now we can find that Carlo has 4 – 2¹/₄ = 1³/₄  tubs left.

 Middle School:

Question: Tyler shot 7 rolls of film. On each of the first 3 rolls, 16 photos turned out. Fourteen photos turned out on each of the next 4 rolls. If Tyler shoots 1 more roll of film, how many photos need to turn out for Tyler to have an average of 17 successful photos per roll?

Answer:  22 photos

Solution:  Tyler already has 3 × 16 + 4 × 14 = 104 good pictures. To average 17 good pictures per roll, he needs 17 × 8 = 136 pictures to turn out in total. So, Tyler needs 136 – 104 = 22 photos on the 8th roll to turn out.

Algebra and Up: 

Question: Mia has two cans of purple paint and a can of white paint. One of the purples is 30% red and 70% blue. The other is 50% red and 50% blue. If Mia wants 8 fluid ounces of a mixture that is 20% red, 30% blue, and 50% white, how many fluid ounces of each kind of paint does she need?

Answer:  2 fluid ounces of 30% / 70%, 2 fluid ounces of 50% / 50%, and 4 fluid ounces of white.

Solution:  We know right off the bat that we need 4 ounces of white paint because 50% of 8 ounces is 4 ounces. So, next we need to find out what amounts of the two purple paints to mix together to make 4 ounces of a 40% red, 60% blue paint (we need to double the percentages because we’re only dealing with the half that isn’t white). We can see that the average of 30% red and 50% red is 40% red, so we need equal parts of the first and second paints. That’s 2 ounces of each to make 8 ounces total. Alternatively, we could use the equation 50%(4-x) + 30%x = 4(40%) wherein x represents the amount of the first paint.

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

In this circle puzzle, dashed arrows indicate addition while solid arrows indicate multiplication. Which number will replace the question mark?

Answer: 56