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.
