Question

A printer will produce 80 wedding invitations for $210. The price to produce 120 invitations is $290. The printer uses a linear function to determine the price for producing different amounts of invitations. How much will the printer charge to produce 60 invitations?
A)$120.00
B)$145.00
C)$157.50
D)$170.00

Answer 1

Answer:  Option 'D' is correct.

Step-by-step explanation:

Let the number of wedding invitations be represented by x axis.

Let the cost of wedding invitations be represented by y-axis.

So, At cost of $210, a printer will produce 80 wedding invitations.

At cost of $290, a printer will produce 120 wedding invitations.

So, we have (80,210) and (120,290)

So, our equation of slope will become:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-210=\frac{290-210}{120-80}(x-80)\\\\y-210=\frac{80}{40}(x-80)\\\\y-210=2(x-80)\\\\y-210=2x-160\\\\y=2x-160+210\\\\y=2x+50$

We need to find the cost of 60 (= x) invitations:

$y=2x+50\\\\y=2\times 60+50\\\\y=120+50\\\\y=\ 170$

Hence, Option 'D' is correct.

Answer 2

Answer:

The printer charge is $170 to produce 60 invitations.

Step-by-step explanation:

A printer will produce 80 wedding invitations for $210

$(x_1,y_1)=(80,210)$

The price to produce 120 invitations is $290.

$(x_2,y_2)=(120,290)$

We will use two point slope form

Formula : $y- y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Substitute the values :

$y- 210=\frac{290-210}{120-80}(x-80)$

$y- 210=2(x-80)$

$y- 210=2x-160$

$y- 210=2x-160$

$y=2x+50$

Now we are supposed to find the printer charge to produce 60 invitations

Substitute x = 60

$y=2(60)+50$

$y=170$

Hence the printer charge is $170 to produce 60 invitations.