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Common Misconceptions (Algebra)

Arm yourself with the tools to be the king or queen of heady mathematical debates, like the age old question of whether 0.999.... = 1.

Setting Up Equations Misconceptions


It takes 4 cooks 4 hours to bake 4 cakes. Assuming no change of rate, how many hours will it take 8 cooks to bake 8 cakes?

Amy has a 3600 square foot apartment that she wants to carpet. The carpeting company informs her that it will cost $200 plus $30 per square yard. How much will it cost to carpet her entire apartment?

Note: 1 yard = 3 feet.

Mary’s storage locker is full of sports equipment. She’s interested in the total number of tennis rackets and tennis balls that she has, so she sends her assistants to count them.

Her first assistant returns and tells her that she would have twice as many rackets as balls, except she found an extra package of 6 balls in the back.

Since that wasn’t enough information, she sent her second assistant out to count them. He returns and informs Mary that if she had three more balls, she would have half as many balls as rackets.

Does Mary have enough information now to determine how many rackets she has?

During a basketball game, a basketball player made 15 baskets. Each basket was worth either 2 or 3 points (no 1-point free throws). The player scored 40 total points. You want to figure out how many 3-point baskets that player made. Which system of equations correctly models this situation?

A. Call the number of 2-point shots the player made \(x\) and the number of 3-point shots \(y.\) The system of equations is: \[x+y = 15\] \[2x+3y=40\]

B. Call the total number of points scored from 2-point shots \(a\) and the total number of points from 3-point shots \(b.\) The system of equations is: \[a+b=40\] \[\frac{a}{2} + \frac{b}{3} = 15\]

You are baking lemon muffins for a breakfast meeting with 16 total attendees, when you realize that you are out of lemon zest. You need a quarter cup of lemon zest per batch, and you want to make enough 24-muffin batches so that everyone at the meeting can have 3 muffins.

However, lemon zest is only sold in 4 fl. oz. packages. How many packages do you need to buy to make enough muffins for everyone?

Note: There are 8 fl. oz. in one cup.


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