Lower Elementary:
Question: Gloria is selling flowers. On Monday, she sells 10 flowers. On Tuesday, she sells 15 flowers. If she sells the flowers for $2 a flower, how much money will Gloria have at the end of Tuesday?
Answer: $50
Solution: First, let’s figure out how many flowers Gloria sold in all. 10 + 15 = 25. Gloria sold 25 flowers. Since she sells each flower for $2 each, to find how much money she earned in total, double the total number of flowers. 25 doubled is 50. She earned a total of $50.
Upper Elementary:
Question: A basketball game is 80 minutes long. If it is half way through the third quarter, how much of the game is left?
Answer: 30 minutes
Solution: Let’s figure out how many minutes are in each quarter. A quarter of something is the same as taking half of a half. Half of 80 is 40, and half of 40 is 20. So, each quarter is 20 minutes. If we are half way through the third quarter, that means we have half of a quarter and then the last quarter to go until the end of the game. Half of a quarter of the game is 10 minutes long (half of 20 minutes). So, there are 30 minutes left in the game (10 + 20 = 30 minutes).
Middle School:
Question: How many even 3-digit whole numbers have non-zero digits?
Answer: 324
Solution: One way to solve this is to figure out the number of possibilities for each digit of the number. For the first digit, it cannot be a zero, so we have 9 choices for digits. For the second digit, it also cannot be zero, so we have 9 choices for digits. For the last digit, it has to be even so we have 5 choices (0, 2, 4, 6, 8). But it also cannot be zero, so there are actually only 4 choices. The total number of 3 digit numbers is 324 (9 × 9 × 4).
Algebra and Up:
Question: Find the equation of the line that is perpendicular to and has the same x-intercept as the line 3y = –6x + 12.
Answer: y= 1/2x – 1
Solution: First, we can simplify the given line by dividing both sides by 3. The simplified equation is y = –2x + 4. The x-intercept is the point found by plugging in 0 for y and solving for x.
0 = –2x + 4
2x = 4
x = 2
The x-intercept is 2, meaning that the line passes through the point (2, 0). To find a perpendicular slope, take the negative reciprocal of the given slope. The slope of the given line is –2. The negative reciprocal is 1/2, so the perpendicular slope is 1/2. Now we have a point (2, 0) and a slope of 1/2. By plugging this information into point-slope form, we can find the equation of the line.
y – y1 = m(x – x1)
y – 0 = 1/2(x – 2)
y – 0 = 1/2x – 1
y = 1/2x – 1
The equation of the line that is perpendicular to and has the same x-intercept as the line 3y = –6x + 12 is y= 1/2x – 1
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