Lower Elementary:
Question: Valerie sent 56 emails on Monday. On Tuesday, she sent half as many emails as she sent on Monday. On Wednesday, she sent half as many emails as she did on Tuesday. How many emails did Valerie send on Wednesday?
Answer: 14 emails
Solution: In order to find out how many emails Valerie sent on Wednesday, we need to know how many emails she sent on Tuesday. Valerie sent half as many emails on Tuesday as she did on Monday. Half of 56 = half of 50 + half of 6 = 25 + 3 = 28. Valerie sent 28 emails on Tuesday. She sent half as many emails on Wednesday as she did on Tuesday. Half of 28 = half of 20 + half of 8 = 10 + 4 = 14. Valerie sent 14 emails on Wednesday.
Upper Elementary:
Question: Henry needs to buy enough AA batteries to replace them all in his remotes. He has four remotes that need 2 AA batteries each and four other remotes that need 3 AA batteries each. A pack of 4 AA batteries cost $6. How much money does Henry need to buy enough batteries to replace the batteries in all 8 remotes?
Answer: $30
Solution: First, we need to find the total number of batteries that Henry needs. There are 4 remotes that need 2 AA batteries each. 4 × 2 = 8. Henry needs 8 batteries for those 4 remotes. The other 4 remotes need 3 AA batteries each. 4 × 3 = 12. Henry needs 12 batteries for the other 4 remotes. This means that Henry needs a total of 20 batteries (8 + 12 = 20). Each pack of 4 AA batteries cost $6. If we count in groups, we see that 8 AA batteries cost $12, 12 AA batteries cost $18, 16 AA batteries cost $24, and 20 AA batteries cost $30.
Middle School:
Question: The Leone family wants to know who used the most data for their family data plan. Of the total data, Nancy used 0.18. Hank used 1/4 of the data. Sammy used 30% of the data. Michael used the rest of the data. Who used the most data?
Answer: Sammy
Solution: In order to compare the amount each person used, we need to have each part be represented as either a decimal, a fraction, or a percent. Let’s convert everything to a percent. Percent means for each hundred. To convert a decimal to a percent, we move the decimal to the right 2 places. 0.18 = 18%. Nancy used 18% of the data. One way to convert a fraction to a decimal is to find an equivalent fraction so that the denominator is 100. 1/4 = 25/100. So Hank used 25% of the data. Sammy used 30% of the data. To find the part that Michael used, we take the sum of the other parts and subtract it from 100%, or the whole. 18 + 25 + 30 = 73. 100 – 73 = 27. So, Michael used 27% of the data. This means that Sammy used the most data.
Algebra and Up:
Question: The speed at which a car is travelling is given by s = d/t where s is speed, d is distance traveled, and t is time elapsed. A car starts a trip by going at a constant speed of 57 miles per hour for 114 miles. It then increases its speed to 60 miles per hour until it reaches its destination. The entire trip was 384 miles. How long did the trip take?
Answer: 6 and a half hours
Solution: First we need to find how long the car was traveling when it was going 57 miles per hour. To find the time it takes, take the distance traveled and divide by the speed the car was traveling. 114 / 57 = 2. It took 2 hours to go the first 114 miles. The entire trip was 384, but the first 114 miles were traveled at a different speed. 384 – 114 = 270. The car was traveling at 60 miles per hour for 270 miles. 270 / 60 = 4.5. It took 4.5 hours for the car to travel the remaining 270 miles. Therefore, the entire trip took 2 + 4.5 = 6.5 hours.
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