Lower Elementary:
Question: Kyle looked at the time and it was 4:26. He then listened to two songs. The first song lasted 3 minutes and 37 seconds and the second song lasted 4 minutes and 23 seconds. What time was it when the second song ended?
Answer: 4:34
Solution: One way to solve this problem is to determine how much time passed while both songs played. The first song played for 3 minutes and 37 seconds and the second song played for 4 minutes and 23 seconds. If we add the seconds first, we have 37 + 23 = 60 seconds. 60 seconds = 1 minute, so we add 1 minute to the total. 3 minutes + 4 minutes + 1 minute = 8 minutes. 8 minutes past 4:26 is 4:34, so the time after the two songs played was 4:34.
Upper Elementary:
Question: Carly had 7 chocolate bars at the beginning of the week. She ate half of the candy bars on Monday and then she ate half of what was remaining on Tuesday. How much chocolate does she have left on Wednesday?
Answer: 1 3/4 chocolate bars
Solution: On Monday, Carly ate half of the 7 chocolate bars that she had. Half of 7 = half of 6 + half of 1 = 3 + 1/2 = 3 1/2. She then ate half of what was remaining on Tuesday. Half of 3 1/2 = half of 3 + half of 1/2 = 1 1/2 + 1/4 = 1 3/4. Carly has 1 3/4 chocolate bars left.
Middle School:
Question: Ben is planning on taking the bus from Los Angeles to San Francisco. When he checked the price of bus tickets on Monday, it was $25. When he checked again on Friday, there was a 35% increase in the price. How much did the ticket cost on Friday?
Answer: $33.75
Solution: One way to solve this problem is to find the percent of increase and then add that to the original price. Percent means for each hundred. Since we are trying to find 35%, we count 35 for each 100. Notice that 25 is 1/4 of 100, so to find 35% of 25, we can find 1/4 of 35. To find a quarter of a number, we can take half of a half. Half of 35 = half of 30 + half of 5 = 15 + 2 1/2 17 1/2. Half of 17 1/2 = half of 10 + half of 7 + half of 1/2 = 5 + 3 1/2 + 1/4 = 8 3/4 = 8.75. So, 1/4 of 35 is 8.75. Alternatively, to find the percent of increase, we can multiply the original cost by the percent of increase. 25 × 0.35 = 8.75. So, the price increased by $8.75. To find the new cost, add the price increase to the original price. 8.75 + 25 = 33.75. The new cost of the bus ticket is $33.75.
Algebra and Up:
Question: The sum of three consecutive odd numbers is 255. What are the three numbers?
Answer: 83, 85, and 87
Solution: Let x be the smallest of the three numbers. Since we are looking for consecutive odd numbers, the next number will be x + 2. To get the third number, we would add another 2, which will be (x + 2) + 2 = x + 4. We know what the sum of the three numbers are, so let’s add them together to create an equation and solve for x.
x + x + 2 + x + 4 = 255
Combine like terms.
3x + 6 = 255
Subtract 6 from both sides.
3x = 249
Divide both sides by 3.
x = 83
So the smallest number in the list is 83. The next odd number will be 85, and the last one will be 87. So the three consecutive odd numbers whose sum is 255 is 83, 85, and 87.
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