#### #MathTricks: Divisibility

To test if a number is divisible by 11, follow the general rule: the difference of the sum of alternating digits can be divided by 11. To determine if the number 2,728 is divisible by 11, find the difference of the ..

Money is an important part of everyday life, and it just makes sense to know the function of dollars and cents.

This week’s word problems focus on understanding value and calculating purchases. Read the problems below and choose the one that’s the right skill level for your child. Have them give it a try. And when they feel they’ve found the answer, check their solution against ours on the next page.

**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?

**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?

**Middle School:**

*Question:* Logan 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?

**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?

Excellent! Are you ready to check your answer? Look below to see if your solution matches ours.

**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).