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News from Mathnasium of West Lexington

Probelms of the Week Answers (August 28th)

Aug 29, 2017

Lower Elementary:

Question: Jack decides to paint the walls in his bedroom with colorful stripes. The first stripe in the pattern is red, then orange, then yellow, then orange, then red, then orange, then yellow, then orange, and so on. If the pattern continues, what color will the 30th stripe be?

Answer:  Orange

Solution:  The pattern repeats every four stripes—red, orange, yellow, orange. That means that the pattern completes itself 30 ÷ 4 = 7 whole times with a remainder of 2 stripes. So, the pattern completes on the 28th stripe, then we start again at red on the 29th stripe, and orange on the 30th.


Upper Elementary:

Question: Nora makes 90 homemade crayons. A small box can hold 8 crayons, and a large box can hold 24 crayons. If she fills 4 small boxes with crayons, how many large boxes will she need for the rest of the crayons? 

Answer:  3 large boxes

Solution:  Four small boxes hold 8 × 4 = 32 crayons, leaving 90 – 32 = 58 crayons unboxed. So, Nora can put 48 into 2 large boxes and the rest into a 3rd large box.


Middle School:

Question: Micah sculpts two statues, one of a dog and one of a cat. The real-life dog weighs 20 pounds, and its statue weighs 48 pounds. The real-life cat weighs 15 pounds. If the statues are both proportional to the animals in weight, then how much does the cat’s statue weigh?

Answer36 pounds

Solution:  Since 20 ÷ 48 = 5/12, the ratio of the animals’ weight to their statues’ must be 5:12. The cat weighs 15 pounds, so its statue’s weight must be 36 pounds because 5:12 = 15:36.


Algebra and Up:

Question: The value of a painting increased by 20% after the painter appeared on a popular talk show. The value of the painting increased again by 15% when the painter was featured in a magazine. If the value of the painting is now $1,242.00, what was its original value?

Answer:  $900.00

Solution:  The value increased by 20%, then the percent increase was compounded by another 15%. So, if we call the original value of the painting x, we can set up an equation:

x(1.20)(1.15) = $1,242.00

1.38x = $1,242.00

x = $900.00