Lower Elementary:
Question: Joey has 7 coins. 3 are nickels and the rest are dimes. How much money does Joey have?
Answer: 55¢
Solution: If Joey has 3 nickels and has a total of 7 coins, then that means he has 4 dimes (7 – 3 = 4). One nickel is worth 5¢, two nickels are worth 10¢, and three nickels are worth 15¢. One dime is worth 10¢, two dimes are worth 20¢, three dimes are worth 30¢, and four dimes are worth 40¢. Since three nickels are worth 15¢ and four dimes are worth 40¢, that means he has a total of 55¢.
Upper Elementary:
Question: If you needed to buy 24 batteries, what would be the better buy and by how much: buying 6-packs of batteries for $12 each or buying 8-packs of batteries for $15 each?
Answer: 3 8-packs of batteries by $3
Solution: First, we need to find the total cost of buying the 24 batteries in each scenario. To make 24, we need to buy four 6-packs (6 × 4 = 24). One 6-pack of batteries cost $12, so four 6-packs of batteries cost $48 (12 × 4 = 48). To make 24, we need to buy three 8-packs (8 × 3 = 24). One 8-pack of batteries is $15, so three 8-packs of batteries is $45 (15 × 3 = 45). Since the four 6-packs of batteries cost $48 and the three 8-packs of batteries cost $45, the three 8-packs are a better buy because it is $3 cheaper.
Middle School:
Question: What was the original price of a pair of pants that was 15% off and its discounted price is $51?
Answer: $60
Solution: One formula for finding the discount price is (original price)(1 – percent discount) = (discount price). Since we are given what the discount price and the percent is, we can substitute these values into the formula to find the original cost.
(original cost)(1 – 0.15) = 51
Simplify the parenthesis.
(original cost)(0.85) = 51
Divide both sides by 0.85.
original cost = 60.
The original cost of the pair of pants is $60.
Another way of solving this problem is to find the whole given the percent and the part. Since it is 15% off, that means that the discounted price is 85% off of the original price. 85% of what number is 12. Let n be the number.
0.85n = 51
Divide both sides by 0.85.
n = 60.
The original cost of the pair of pants is $60.
Algebra and Up:
Question: The sum of 3 consecutive odd integers is –93. What are the three numbers?
Answer: –33, –31, –29
Solution: Let n be the first odd integer. The second number is the next odd integer, which can be found by adding 2 to the first term. So, the second term in n + 2. Similarly, the third term is found by adding 4 to the first term. So, the third term is n + 4. Adding all of these values together, we have that:
n + n + 2 + n + 4 = –93
Combine the like terms.
3n + 6 = –93
Subtract 6 from both sides.
3n = –99
Divide both sides by 3.
n = –33
So the first number is –33. This means that the second number is –31 and the third number is –29.
