Question

assignment
linear equations and inequalities
or questions 15 and 16 create an equation for the problem and solve it. show all your
work. write your answer in a sentence.
. we arrived in drumheller while the badlands passion play was on. it is an
outdoor event. we saw the performers light two different sizes of candles.
the 12 cm candles burned at 0.5 cm per hour and the 18 cm candles burned
at 2 cm per hour. how many hours did it take the two candle sizes to burn to the
same size?
6 marks — 1 mark for each step and 1 mark for sentence.

Explanation:

Step1: Define variable

Let \( h \) be the number of hours passed.

Step2: Equation for 12cm candle

The length of the 12cm candle after \( h \) hours is \( 12 - 0.5h \) (since it burns at 0.5 cm per hour).

Step3: Equation for 18cm candle

The length of the 18cm candle after \( h \) hours is \( 18 - 2h \) (since it burns at 2 cm per hour).

Step4: Set equations equal

To find when they are the same size, set \( 12 - 0.5h = 18 - 2h \).

Step5: Solve for h

Add \( 2h \) to both sides: \( 12 + 1.5h = 18 \).
Subtract 12 from both sides: \( 1.5h = 6 \).
Divide by 1.5: \( h = \frac{6}{1.5} = 4 \).

Answer:

It took 4 hours for the two candle sizes to burn to the same size.