SOLUTION: I'm trying to help my son with his homework, but I'm not sure how to set up the following problem into an algebraic model. I looked at some of the examples in the book, but they ju

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Question 60414This question is from textbook California Middle School Mathmatics Concepts and Skills Course 2
: I'm trying to help my son with his homework, but I'm not sure how to set up the following problem into an algebraic model. I looked at some of the examples in the book, but they just confuse me. I hope you can help us.
The problem is: Suppose you light one candle that is 12 centimeters tall and burns at a rate of 3 centimeters per hour. At the same time, a friend lights a candle that is 10 centimeters tall and burns at a rate of 2 centimeters per hour.
Write and solve an algebraic model to find when the heights of the candles will be the same. This question is from textbook California Middle School Mathmatics Concepts and Skills Course 2

Found 2 solutions by funmath, ptaylor:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is: Suppose you light one candle that is 12 centimeters tall and burns at a rate of 3 centimeters per hour. At the same time, a friend lights a candle that is 10 centimeters tall and burns at a rate of 2 centimeters per hour.
Write and solve an algebraic model to find when the heights of the candles will be the same.
:
The candles are starting at a certain height and losing so much height per hour.
Let time be:x
The first candle: 12-3x
The second candle: 10-2x
The same means: =
:
12-3x=10-2x
:
12-3x+3x=10-2x+3x
12=10+x
12-10=10-10+x
2=x
:
They'll be the same height in 2 hours.
Happy Calculating!!!

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Lets work this problem two ways:
First, let x=the number of hours that have elapsed at the time when the candles are the same height.
At this time, the 12cm candle is 12-3x cm tall and
the 10cm candle is 10-2x cm tall. If they are the same height, then these two quantities must be equal and our equation is:
12-3x=10-2x; and solving, we have x=2 hours
This problem can also be worked graphically: Draw a 12cm rectangle and a 10cm rectangle beside each other. Put lines across the 12cm rectangle at 3cm intervals and put lines across the 10cm rectangle at 2cm intervals and note where the lines coincide.
Hope this helps -----ptaylor