Lower Elementary
Question: Wanda sells cups of lemonade for 50¢ each. How many cups of lemonade did Wanda sell if she made $4.00?
Answer: 8 cups
Solution: 50¢ doubled is $1, so we can also say that Wanda sells 2 cups of lemonade to make $1. Since $1.00, four times is $4.00, she sold 2 cups of lemonade, 4 times, which is 8 cups.
Upper Elementary
Question: Gary is getting in shape for football season. He starts by doing 5 sets of 15 push-ups. After doing other exercises, he cools down be doing an additional 10 push-ups. How many total push-ups did Gary do?
Answer: 85 push-ups
Solution: To see how many push-ups Gary did before the rest of his routine, multiply 15 by 5. 15 × 5 = 75. He does 10 push-ups to cool down, so add 10 to get the total number of push-ups Greg does. 75 + 10 = 85 push-ups.
Middle School
Question: You are making a 4 digit code for your bike lock. No digit can be repeated. The first digit is a 1. The second digit must be a prime number. How many different combinations are there for the bike lock code?
Answer: 224 combinations
Solution: There are 10 digits to choose from (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). The first digit must be 1, so there is only one choice. The second digit is a prime number, so our choices are 2, 3, 5, and 7. Thus we have 4 choices for the second digit. The third digit can be anything not repeated. Since we already used 2 digits, there are 8 to choose from for the third digit. Likewise, there will be 7 digits to choose from for the fourth digit. To find the total number of combinations, multiply all of the possibilities for each digit together. 1 × 4 × 8 × 7 = 224
Algebra and Up
Question: Where will the lines y = 3x + 2 and y = –2x + 7 intersect?
Answer: (1,5)
Solution: Asking where two lines intersect is the same as solving the system of linear equations. One way to solve this problem is to set both equations equal to each other (since both equations have y by itself on one side).
3x + 2 = –2x + 7
Solve for x:
5x = 5
x = 1
Now that we know x, plug it into either equation to solve for y.
y = 3(1) + 2
y = 5
So, the two graphs will intersect at the point (1,5).
