News from Mathnasium of Middletown KY
Problem of the Week 05-16-16
May 18, 2016
Question: Ellie breaks open her piggy bank and finds the coins below. 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.
Question: Packs of trading cards cost $3.50. How many packs of trading cards can Max buy with a $20 bill?
Answer: 5 packs
Solution: First, let’s estimate how many packs of cards Max 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, five times is $17.50. That means that if Max buys 5 packs, he’ll have $2.50 left, which isn’t enough to buy another pack of cards. So, Max can buy 5 packs of cards at most.
Question: Harrison bought a box of 64 colored pencils for $24.00 and a box of 36 crayons for $12.60. Which cost more, a single colored pencil or a single crayon?
Answer: A 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 = 37.5¢. Let’s compare to the price of a crayon, which is $12.60 ÷ 36 = 35¢. The value of a 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 right now, how much was it worth exactly 50 years ago?
Solution: We can model the increasing value of the painting with the expression x • 1.0250, wherein x is the starting value of the painting, 1.02 represents the percent increase, and 50 is the elapsed time. We know that after the 50 years, the painting is worth $1,000, so $1,000 = x • 1.0250. To solve for x, we divide: $1,000 ÷ 1.0250 = $371.53. (Remember to round up to the next cent!)
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