Lower Elementary:
Question: Dolores has 45 flowers. She used 7 of the flowers to make a bouquet. She then used half of the remaining flowers to make a wreath. How many flowers does Dolores have left?
Answer: 19 flowers
Solution: Dolores started with 45 flowers and used 7 of the flowers to make a bouquet. 45 – 7 = 38. She has 38 flowers left after making the bouquet. She used half of the flowers to make a wreath. Half of 38 is 19 (half of 38 = half of 30 + half of 8 = 15 + 4 = 19). There are 19 flowers left.
Upper Elementary:
Question: Vince is making goody bags to give to his friends. He bought 5 bags of candy. Each bag contains 20 pieces of candy. He wants to put 4 pieces of candy in each goody bag. How many goody bags does Vince need to use up all of the candies?
Answer: 25 goody bags
Solution: One way to solve this is to start by calculating the total number of candy. To find the total number of candy, multiply the number of bags of candy by the number of pieces of candy in each bag. 5 × 20 = 100. Vince has 100 total pieces of candy. To see how many goody bags Vince needs, divide the total number of pieces of candy by the number he puts in each bags. 100 ÷ 4 = 25. Vince needs 25 goody bags for all of the candies.
Middle School:
Question: Riley has 1,000 sunflower seeds. He eats 20% of the sunflower seeds on Monday. He eats 1/4 of the original amount of sunflower seeds on Tuesday. How many sunflower seeds are left after Tuesday?
Answer: 550 sunflower seeds
Solution: One way to solve this is to calculate the decimal part of the sunflower seeds that Riley has eaten. 1/4 is equivalent to 25/100, so 1/4 written as a percent is 25%. If Riley ate 20% on Monday and 25% on Tuesday, then the total percent of sunflower seeds he ate is 45%. That means he did not eat 55% of the seeds. Percent means for each hundred. There are 10 hundreds in 1,000. So 55% of 1,000 is 550. There are 550 sunflower seeds left.
Algebra and Up:
Question: Liza left home and walked along a straight path at a constant rate of 2 feet per second. Her sister Becky saw that Liza left her phone at home, and so ran after her to return it. She left 30 seconds after Liza did and ran at a constant rate of 5 feet per second. If they continue at their pace, how long will it take Becky to catch up with Liza?
Answer: 20 seconds
Solution: Let’s have t = the time elapsed since Liza left her home and have D = the distance traveled. One way to solve this problem is to relate the scenario as a linear equation.
Becky’s equation:
When Becky starts leaving from home, she is traveling at a rate of 5 feet per second. So her distance traveled is D = 5t
Liza’s equation:
From the time Becky starts leaving the house, Liza traveled 60 feet (2 feet per second times 30 seconds is 60 feet). So the distance traveled by Liza when Becky leaves the house is D = 2t + 60.
Since we are trying to find the time when they meet, we want D to be the same for both. So, we will set the equations equal to each other and solve for t to find the amount of time Becky takes to catch up to Liza.
5t = 2t + 60
Subtract 2t from both sides
3t = 60
Divide both sides by 3
t = 20
It will take 20 seconds for Becky to catch up with Liza.
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