Lower Elementary:
Question: A pencil costs 50¢ and a notepad costs 75¢. How much do 3 pencils and 2 notepads cost altogether?
Answer: $3
Solution: First we need to find the cost of each item separately. One pencil costs 50¢, so count by 50, three times to find the cost of 3 pencils. 50, 100, 150. 3 pencils cost a total of $1.50. One notepad is 75¢, so double 75¢ to get the cost of 2 notepads. 75 doubled = 70 doubled + 5 doubled = 140 + 10 = 150. 2 notepads cost $1.50. Add them together to find the total. $1.50 + $1.50 = $3.
Upper Elementary:
Question: Kyle has two options he can do with his $50. He can either double it first and then earn another $25 or he can earn $15 first and then double his total amount. Which option would give Kyle more money and by how much?
Answer: Adding $15 and then doubling; he earns $5 more
Solution: Let’s see how much Kyle will earn with each method separately. The first option doubles his $50 and then adds $25. $50 doubled is $100. $100 + $25 = $125. The second option adds $15 and then doubles the new amount. $50 + $15 = $65. 65 doubled = 60 doubled + 5 doubled = 120 + 10 = 130. Kyle will earn $125 with the first option and $130 with the second option. Therefore, the second option of adding $15 and then doubling will give more money by $5 (130 – 125 = 5).
Middle School:
Question: An empty rectangular pool has a volume of 4,000 feet cubed. It is 10 feet deep and its length and width are the same. What is the perimeter of the pool?
Answer: 80 feet
Solution: First, we need to find the length and width of the pool. The pool has a volume of 4,000 feet cubed, and we know it is 10 feet deep. That means if we divide the volume by the depth, we will have what the length times the width of the pool is, which is the area of the top of the pool. 4,000 ÷ 10 = 400. The area of the top part of the pool is 400 feet squared. Since we are told that the length and the width are the same, that means the top of the pool must be a square. So to find the length and width of the pool, we have to take the square root of the area. The square root of 400 is 20 since 20 × 20 = 400. Therefore, the length and the width of the pool are 20 feet. To find the perimeter, add all of the sides. There are 4 sides, and each side is 20 feet. 20 × 4 = 80. The perimeter of the pool is 80 feet.
Algebra and Up:
Question: The weight of a bowl and the candies in the bowl is 2 pounds. 5/8 of the candies are eaten, and now the bowl and the remaining candies weigh 1.25 pounds. What is the weight of the bowl?
Answer: 4/5 or 0.8 of a pound.
Solution: Let’s have b = the weight of the bowl and c = the weight of the candies. We know together in the beginning they weighed 2 pounds, so we have that b + c = 2. If 5/8 of the candies are eaten, then that means 3/8 of the candies remain. So, we have that b + 3/8c = 1.25. So the system of equations that we have are:
b + c = 2
b + 3/8c = 1.25
We want to know the weight of the bowl, so we want to solve for b. One way to start is to multiply the bottom equation by 8 to remove the fraction.
b + c = 2
8b + 3c = 10
To solve for b, we have to cancel out the c’s. We can do this by multiplying the top equation by –3.
–3b – 3c = –6
8b + 3c = 10
Add the equations together.
5b = 4
Divide by 5.
b = 4/5 = 0.8
The bowl weighs 4/5, or 0.8, of a pound.
