Lower Elementary
Question: Jeremy went with his mom to buy school supplies. They bought a box of pencils for $3.00, an eraser for 30¢, and a binder for $6.45. How much money did they spend on Jeremy’s school supplies?
Answer: $9.75
Note: To find how much money was spent on Jeremy’s school supplies, we add the cost of the pencils, the cost of the eraser, and the cost of the binder together.
$3.00 + $0.30 + $6.45 = $9.75
Upper Elementary
Question: During the summer break Winnie read 5 more books than Kevin. Together they read 19 books. How many books did Kevin read?
Answer: 7 books
Note: Although this problem could be solved using the guess and check method we could also use another method. Start by subtracting the difference in books read between the two children (5) from the total books read (19).
19 – 5 = 14.
Then we divide the left over books equally between Winnie and Kevin.
Half of 14 = 7
At this point Winnie has 7 books and Kevin has 7 books. Since Winnie read 5 more books than Kevin, we add the 5 books we subtracted from 19 to Winnie’s books giving her 12 books.
That means Kevin read 7 books and Winnie read 12 books.
7 books + 12 books = 19 books
Middle School
Question: Jamie has an average of 87 for the first three tests in his math class. If he gets a 100 on his next two tests, what will his average be for all five tests?
Answer: 92.2
Note: We must first find the total points Jamie scored on his first three tests. Because he scored an average of 87 points, to find the total points of his first three tests we add 87 three times.
87 + 87 + 87 = 87 x 3 = 261 points
If Jamie gets a 100 on his next two tests, then adding the scores for these two tests to the total for first three tests will give us the total points Jamie would earned on all five tests.
261 + 100 + 100 = 461 points
Now we divide his total points by the number of tests he will have taken to find his new average test score.
461 ÷ 5 = 92.2
Algebra and Up
Question: Working together a carpenter and his apprentice can build a bookcase in 2 2/5 hours. If it takes the carpenter 3½ hours to build the bookcase on his own, how long will it take his apprentice to build the bookcase working on his own?
Answer: 7 7/11 hours
Note: Let C equal the time it takes for the carpenter to build a bookcase on his own, let A equal the time it takes for the carpenter to build a bookcase on his own, and let t equal the time it takes for them to complete it together.
So,
C = 3½ = 7/2
t = 2 2/5 = 12/5
A = ?
This is a “work” problem. To find how long it will take the apprentice to do the job on his own, we need to convert the work rates to how much work is done in a single hour. In one hour the carpenter does 1/7/2 or 2/7 of the job. We can check this by adding 2/7 three and a half times.
2/7 + 2/7 + 2/7 + 1/7 =7/7 = 1 job
Together they do 1/5/12 or 5/12 of the job every hour. The apprentice can do 1/A of the job per hour.
Adding work rates per hour of the carpenter and the apprentice and setting it equal to the work rate per hour when they work together allows us to solve for the total time it will take the apprentice to finish the job on his own.
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