Lower Elementary:
Question: Mackenzie buys some chips that cost a total of $2.33. She gives the cashier a one dollar bill and six quarters. How much change will Mackenzie receive?
Answer: 17 cents
Solution: First, we need to see how much money Mackenzie paid. She paid a one dollar bill which is $1 and then 6 quarters. One quarter is worth 25¢, two quarters are worth 50¢, three quarters are worth 75¢, four quarters are worth $1, five quarters are worth $1.25, and six quarters are worth $1.50. So Mackenzie paid a total of $2.50 ($1 + $1.50 = $2.50). Because the chips cost $2.33, Mackenzie will get 17¢ back as change ($2.50 – $2.33 = 17¢).
Upper Elementary:
Question: At a bake sale table, a third of the items are brownies, a sixth of the items are lemon squares, and the remaining 45 items are cookies. How many total items are there on the bake sale table?
Answer: 90 items
Solution: First, we have to find the fractional part of the bake sale items that the cookies represent. To do that, we take one whole and subtract the sum of the other parts. In order to add 1/3 and 1/6, we need them to have the same name or common denominator. 1/3 = 2/6, so now we can add them. 2/6 + 1/6 = 3/6 = 1/2. One whole take away one half is one half. So the 45 cookies represent 1/2 of the total items at the bake sale table. If half of the total items is 45, then there are 90 total items on the table.
Middle School:
Question: It takes 28 minutes for a tablet to charge from 20% to 60%. At this rate, if the tablet started at 0%, how long will it take for the tablet to fully charge?
Answer: 70 minutes, or 1 hour and 10 minutes
Solution: There is a 40 percentage point difference between 20% and 60% (60 – 20 = 40). This means that 28 minutes represents 40% of the time it takes to charge the tablet. This means that 14 minutes represents 20%. Notice that 40% + 40% + 20% = 100%. So, to find the amount of time it takes to fully charge the tablet, we add the times represented by 40% twice and 20% once. 28 + 28 + 14 = 70. It will take 70 minutes, or 1 hour and 10 minutes, for the tablet to fully charge.
Algebra and Up:
Question: Is (250 – 249)/2 greater than, less than, or equal to 248?
Answer: Equal to
Solution: One way to solve this problem is to try and simplify (250 – 249)/2 to make it easier to compare to 248. One way to simplify it is to factor out a 249 from the numerator.
249 (21 –1)/2
Simplify what is in the parenthesis.
249 (2 – 1)/2
249 (1)/2
249/2
Reduce the fraction.
248
From this, we can see that (250 – 249)/2 simplifies to 248, which is equal to 248.
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