**Lower Elementary:**

*Question: *Penelope has an equal number of pennies and dimes. If she had 77¢, how many coins does Penelope have altogether?

*Answer: *14 coins

*Solution: *A penny is worth 1¢ and a dime is worth 10¢. Since there are an equal number of pennies and dimes and one penny and one dime together is 1¢ + 10¢ = 11¢, we can count by 11 to see how many pennies and dimes there are altogether. 11, 22, 33, 44, 55, 66, 77. That means there are 7 pennies and 7 dimes. So altogether there are 7 + 7 = 14 coins.

**Upper Elementary:**

*Question: *Tracey’s dogs eat 3/10 of a bag of dog food a day. If Tracey has two full bags of dog food, how many full days can Tracey feed her dogs?

*Answer: *6 days

*Solution: *Tracey has 2 bags of dog food. She needs 3/10 of a bag to feed her dogs a day. So to find how many full days Tracey can feed her dogs, we divide the 2 bags of dog food by the 3/10 that Tracey uses a day. 2 ÷ 3/10 = 2 × 10/2 = 20/3 = 6 2/3. Tracey does not have enough for 7 full days, so she has enough for 6 full days.

**Middle School:**

*Question: *The ratio of chocolate chip cookies to oatmeal raisin cookies in a cookie jar is 4:3. If there is a total of 42 cookies in the jar, how many oatmeal raisin cookies are there?

*Answer: *18 oatmeal raisin cookies

*Solution: *Since the ratio is 4:3, that means that for every 7 cookies, 4 of them are chocolate chip cookies and 3 of them are oatmeal raisin cookies. So if we divide the 42 cookies in the jar by 7, then that means there are 6 groups of 4 chocolate chip cookies and 6 groups of 3 oatmeal raisin cookies. This means that there are 6 × 3 = 18 oatmeal cookies.

**Algebra and Up:**

*Question: *The absolute value of twelve less than a number is half of the same number. What are the possible solutions?

*Answer: *8 and 24

*Solution: *Writing the problem as an equation, if n is the number, then we have |n – 12| = (1/2)n. Since it is an absolute value equation we have to find both the positive and the negative solution.

Positive: n – 12 = (1/2)n

Subtract n from both sides.

–12 = –(1/2)n

Multiply both sides by –2.

24 = n

Negative: n – 12 = –(1/2)n

Multiply both sides by –2.

–2n + 24 = n

Add 2n to both sides.

24 = 3n

Divide both sides by 3.

8 = n

When we check both answers, both 8 and 24 work. So the possible solutions are 8 and 24.