Question

The cost for two different companies to make x candles is shown on the graph.

Answer 1

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.