Answer:
D) Quick Wick will make more candles when the cost is $600.
Step-by-step explanation:
Find the initial value (b) and the cost per candle (m), to write the equation of each line in the slope-intercept form, y = mx + b. This will help for easy comparison.
✔️Wax Art:
m = change in y/change in x
Using (10, 140) and (20, 180),
m = (180 - 140)/(20 - 10) = 40/10
m = 4
Cost per candle = $4
To find b, substitute (x, y) = (10, 140) and m = 4 into y = mx + b
140 = 4(10) + b
140 = 40 + b
140 - 40 = b
100 = b
b = 100
Initial value = $100
To get the equation, substitute m = 4 and b = 100 into y = mx + b
y = 4x + 100
✔️Quick Wick:
m = change in y/change in x
Using (10, 120) and (30, 180),
m = (180 - 120)/(30 - 10) = 60/20
m = 3
Cost per candle = $3
To find b, substitute (x, y) = (10, 120) and m = 3 into y = mx + b
120 = 3(10) + b
140 = 30 + b
120 - 30 = b
90 = b
b = 90
Initial value = $90
To get the equation, substitute m = 3 and b = 90 into y = mx + b
y = 3x + 90
Let's analyse each option given using the information we now have:
✔️Option A: INCORRECT
Cost per candle for made is $1 less for Quick Wick. I.e. cost per candle for Quick wick is $3. Cost per candle for Wax Art is $4.
✔️Option B: INCORRECT
Difference between the initial value sof the two companies = $100 - $90 = $10
✔️Option C:
Find the cost of making 50 candles for each company by substituting x = 50 into each of their equations. Thus:
Wax Art => y = 4x + 100
y = 4(50) + 100
y = $300
Wax Art will make 50 candles for $300
Quick Wick => y = 3x + 90
y = 3(50) + 90
y = $240
Quick Wick makes 50 candles for $240
As we can see, Quick wick is making 50 candles at a lower cost than Wax Art.
Therefore, option C is INCORRECT.
✔️Option D: find out how many candles (x) each company will make when the cost is $600.
Substitute y = 600 in each equation of both companies
Wax Art => y = 4x + 100
600 = 4x + 100
600 - 100 = 4x
500 = 4x
500/4 = x
x = 125 candles
Quick Wick => y = 3x + 90
600 = 3x + 90
600 - 90 = 3x
510 = 3x
510/3 = x
x = 170 candles
Quick Wick will make more candles when he cost is $600.
Therefore, option D is the only CORRECT statement of comparison.
