Lower Elementary:
Question: Kelly’s grandmother gave her $1 for her 1st birthday, $2 for her 2nd birthday, $3 for her 3rd birthday, and so on. Her grandmother has just giver her money for her 6th birthday. How much birthday money has she received from her grandmother altogether?
Answer: $21
Solution: Kelly gets money equal to her age on her birthday. On her 6th birthday, she would have received $1, $2, $3, $4, $5, and $6 in total from her grandmother for each of her birthdays. Adding these up, she received a total of $21 from her grandmother.
Upper Elementary:
Question: One box of fish food flakes costs $6 and can feed 4 fish. If you have an aquarium with 12 fish, how much money will you spend to feed the fish?
Answer: $18
Solution: First we need to find out how many boxes of fish food flakes we need. One box feeds 4 fish. To get to 12 fish, we would multiply by 3. So, we would need 3 boxes to feed 12 fish. Each box costs $6, so multiply by 3 to get the total for 3 boxes. $6 × 3 = $18.
Middle School:
Question: Felix’s gas tank is 75% full. He drives enough to use up 6 gallons and now his gas tank is 50% full. How many gallons can Felix’s gas tank hold?
Answer: 24 gallons
Solution: We know there is a 6 gallon difference between 75% and 50%. To find the part that 6 gallons is, subtract the percents. 75% – 50% = 25%. Thus, 6 gallons is 25% of the tank. So now the question becomes “25% of what number is 6?”
Algebraic Solution:
Using the ratio: 25/100 = 6/x
Cross multiply: 25x = 600
Divide: x = 24
Number Sense Solution:
25% means a quarter of it. So to get all of it, multiply by 4. 6 × 4 = 24 gallons
Algebra and Up:
Question: Six less than a positive number squared is five times the same number. What is the number?
Answer: 6
Solution: If we translate the sentence into an equation, it would be
n^2 – 6 = 5n
To solve for n, we will move the 5n to the other side and solve by factoring.
n^2 – 5n – 6 = 0
To factor this, we need two numbers that multiply to –6 and add to –5. –6 and 1 multiply to –6 and add to –5, so the equation factors into:
(n – 6)(n + 1) = 0
Now we set each factor equal to 0 and solve for n.
n – 6 = 0 n + 1 = 0
n = 6 n = –1
Our solutions are 6 and –1. The question stated that it was a positive number, so our answer is 6.
