# Problems of the Week: September 28 - October 2

Sep 30, 2020 | West Marietta

Lower Elementary:

Question: Ellie breaks open her piggy bank and finds a half dollar, two quarters, two dimes, a nickel, and two pennies. How much money does Ellie have?

Solution:  Ellie has 1 half dollar worth 50¢, 2 quarters worth 25¢ each, 2 dimes worth 10¢ each, 1 nickel worth 5¢, and 2 pennies worth 1¢ each. So, Ellie has 50¢ + 25¢ + 25¢ + 10¢ + 10¢ + 5¢ + 1¢ + 1¢ = 127¢.  Since there are 100¢ in a dollar, that means Ellie has \$1 and 27¢, or \$1.27.

Upper Elementary:

Question: Packs of trading cards cost \$3.50. What is the greatest number of packs of trading cards that Kaylee can buy with a \$20.00 bill?

Answer:  5 packs of cards

Solution:  First, let’s estimate how many packs of cards Kaylee can buy by rounding; \$3.50 rounds up to \$4.00, and \$4.00 goes into \$20.00 five times. Let’s try it with the actual value of a pack of cards; \$3.50 × 5 = \$17.50. That means that if Kaylee buys 5 packs, she’ll have \$2.50 left, which isn’t enough to buy another pack of cards. So, Kaylee can buy 5 packs of cards at most.

Middle School:

QuestionLogan buys a box of 64 colored pencils for \$24.00 and a box of 36 crayons for \$12.60. Which costs more, a single colored pencil or a single crayon?

Answer:  a single colored pencil

Solution:  To find the price of each pencil, we divide the total cost of all the pencils by the number of pencils. Each pencil is worth \$24.00 ÷ 64 = 37½¢. Let’s compare to the price of a crayon, which is \$12.60 ÷ 36 = 35¢. Since 37½¢ > 35¢, the value of a colored pencil is greater than the value of a crayon.

Algebra and Up:

Question: The value of a painting increases by 2% each year. If the painting is worth \$1,000.00 today, how much was it worth exactly 50 years ago?