SOLUTION: Cara likes candles. She also likes mathematics and was thinking about using algebra to answer a question that she had about two of her candles. Her taller candle is 16 centimeters

Question 183971This question is from textbook Holt Mathematics-Georgia
: Cara likes candles. She also likes mathematics and was thinking about using algebra to answer a question that she had about two of her candles. Her taller candle is 16 centimeters tall. For each hour it burns, the candle loses 2.5 centimeters in height.
Her short candle is 12 centimeters tall and loses 1.5 centimeters in height for each hour that it burns. I need help to determine whether these two candles would ever reach the same height at the same time if allowed to burn the same length of time. If it is not possible, I need to know why it could not happen and what would need to be true in order for them to be able to reach the same height. We need to use multiple representations, justify your results and explain your thinking. This question is from textbook Holt Mathematics-Georgia

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Cara likes candles. She also likes mathematics and was thinking about using algebra to answer a question that she had about two of her candles. Her taller candle is 16 centimeters tall. For each hour it burns, the candle loses 2.5 centimeters in height.
Her short candle is 12 centimeters tall and loses 1.5 centimeters in height for each hour that it burns. I need help to determine whether these two candles would ever reach the same height at the same time if allowed to burn the same length of time. If it is not possible, I need to know why it could not happen and what would need to be true in order for them to be able to reach the same height. We need to use multiple representations, justify your results and explain your thinking.
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Taller candle DATA:
height when burning = 16 -2.5x where x is hours of burning
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Shorter candle DATA:
height when burning 12 - 1.5 x
-------------------------
When are they the same height?
16 - 2.5x = 12 - 1.5x
4 = x
----
They are the same height when they have both burned for four hours.
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Cheers,
Stan H.
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