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Math Problem Monday - Nov 6th, 2017 | Mathnasium Livermore, CA
Nov 6, 2017
Question: During summer break Richard read half as many books as Brian. Together they read 24 books. How many books did Brian read?
Answer: 16 books
Note: The problem can be solved using the guess and check method.
Question: Michelle and her sister baked 2 dozen cookies. Then, they ate 1/4 of the cookies. After that they baked another dozen cookies. How many cookies do they have now?
Answer: 30 cookies
Note: 2 dozen cookies = 2 x 12 = 24 cookies. They ate 1/4 of the cookies. 1/4 of 24 = 6. That means they had (24 – 6) 18 cookies left. If they bake 1 dozen more. Now they have 18 + 12 = 30 cookies.
Question: 6 slices of pizza and 2 drinks cost $22. 6 slices of pizza and 1 drink cost $20. How much does 1 slice of pizza cost?
Note: There are several ways to solve this problem. One method is guess and check. Another method would be to notice the difference between the 2 priced meals and then taking away 1 drink. The price changed by $2.00. That means one drink costs $2.00.
Since the cost of 6 slices of pizza and 1 drink is $20, we can find the total cost of 6 slices of pizza by subtracting 2 from 20.
20 – 2 = 18. That means 6 x the cost of each slice = 18. To find the cost of each slice divide 18 by 6. 18 / 6 = 3. Each slice is 3 dollars.
The problem could also be solve algebraically. Let p = cost of each slice of pizza and let d = cost of each drink.
Then 6p + 2d = 22 and 6p + (1)d = 20. We can solve this system of equations by substitution or elimination and we find that p = 3 and d = 2.
Algebra and Up
Question: Frank needs to paint the trim on the bottom of a window that is 12 feet from the ground. If Frank’s ladder is 14 feet long, how far from the wall should the base of the ladder be in order for the top of the ladder to meet the wall at the bottom of the window?
(Leave answer in radical form)
Answer: The square root of 52
Note: Using the Pythagorean theorem, we set up the following equation: 122 + x2 = 142, and we solve for x. 144 + x2 = 196. x = square root of 52.
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