Question

Cara's Candles

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. Each
hour which it burns makes the candle lose 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.

Answer 1

Explanation:

Tall candle:

Height = 16 cm

Let x be number of hours

Height that is burnt in 'x' hours = 2.5 *x = 2.5x

Height of the candle after 'x' hours (H) = 16 - 2.5x

When x = 1 ; H = 16 - 2.5*1 = 16 -2.5 = 13.5 cm

x = 2 ; H = 16 - 2.5*2 = 16 - 5 = 11 cm

x = 3 ; H = 16 - 2.5 * 3 = 16 - 7.5 = 8.5 cm

x = 4 ; H = 16 - 2.5*4 = 16 - 10 = 6 cm

x = 5 ; H = 16 - 2.5*5 = 16 - 7.5 = 3.5 cm

x = 6 ; H = 16 - 2.5*6 = 16 - 15 = 1 cm

Short candle:

Height =12 cm

Let x be number of hours

Height that is burnt in 'x' hours = 1.5 *x = 1.5x

Height of the candle after 'x' hours (h) = 12 - 1.5x

When x = 1 ; h = 12 - 1.5*1 = 12 - 1.5 = 10.5 cm

x = 2 ; h = 12 - 1.5*2 = 12 - 3 = 9 cm

x = 3 ; h = 12 -1.5*3 = 12 - 4.5 = 7.5 cm

x = 4 ; h = 12 -1.5*4 = 12 - 6 = 6 cm

x = 5 ; h = 12 -1.5*5 = 12 - 7.5 = 4.5 cm

x = 6 ; h = 12 -1.5*6 = 12 - 9 = 3 cm

x = 7 ; h = 12 -1.5*7 = 12 - 10.5 = 1.5 cm

C) Intersection point of the two equation is an ordered pair that is solution to both equations.

Here, after 4 hours the height of the both the candle is 6 cm

(4 , 6) is the solution of these two equations.

Y-intercept is the point of intersection where x = 0

X-intercept is the point of intersection at x-axis where y = 0

Yes the short candle can burn more than 7 hours. Short candle can burn for 8 hours