SOLUTION: The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of -0.5. See

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of -0.5. See      Log On


   



Question 1154557: The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of -0.5. See the figure below.
Suppose that the height of the candle after 18 hours is 15 centimeters. What was the height of the candle after 15 hours?

Found 4 solutions by Alan3354, josmiceli, ikleyn, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of -0.5. See the figure below.
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No figure.
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Suppose that the height of the candle after 18 hours is 15 centimeters. What was the height of the candle after 15 hours?
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The slope is cm/hr = -0.5
3 hours earlier it was 3*0.5 taller
---> 15 + 1.5 = 16.5 cm

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=+-.5t+%2B+c+
You are given the point:
( 18, 15 )
+15+=+-.5%2A18+%2B+c+
+15+=+-9+%2B+c+
+c+=+24+
The equation is:
+h%28t%29+=+-.5t+%2B+24+
----------------------------
After 15 hrs:
+h%2815%29+=+-.5%2A17+%2B+24+
+h%2815%29+=+-8.5+%2B+24+
+h%2815%29+=+15.5+
'--------------------
check:
( 18,15 )
+h%28t%29+=+-.5t+%2B+24+
+15+=+-.5%2A18+%2B+24+
+15+=+-9+%2B+24+
+15+=+15+
OK

Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.

            In his solution, @josmicely made several errors on the way.

            His check is  FALSE,  also,  and is not  "the check",  at all.

            For correct solution see the post by Alan.


The correct answer is
    after 15 hours, the height of the candle was 16.5 cm.

It is clear practically without calculations.

In  3 hours between  15  hours and  18  hours,  the height of the candle decreases by  0.5*3 = 1.5 cm.

Therefore,  at the  15  hours time moment,  the height of the candle was  15 + 1.5 = 16.5 cm.     ANSWER

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@josmicely, please do not consider my post as a trial to make a war with you.

Simply, at this forum we should have a protection service for visitors from errors of tutors ---

so, I perform this protection service . . . from time to time . . .


Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Height y depends on time x.

Slope -0.5, and point (18,15);
Equation in point-slope form is y-15=-0.5%28x-18%29,
y=-0.5x%2B9%2B15
highlight_green%28y=-0.5x%2B24%29


The question asks for y if x is 15.