# Solutions

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**Lower Elementary:**

*Answer:*$1.27

*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:**

*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:**

*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:**

*Answer:*$371.53

*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 to the next cent).