Question

One printing press has a fixed daily cost of $50 and a variable cost of $1.50 for every 30 pages printed. A second printing press has a fixed daily cost of $10 and a variable cost of $2 for every 30 pages produced. Question Determine the number of pages for which the total daily costs will be the same. A. 80 B. 1,500 C. 2,400 D. 3,900

Answer 1

Answer:

2400 pages

Step-by-step explanation:

Printer 1 :  50+ 1.50/30 x  where x is the number of pages

Printer 2 :  10 + 2/30 x where x is the number of pages

Set them equal

50+ 1.50/30 x  = 10 + 2/30 x

50 + 1/20x = 10 +1/15 x

Subtract 1/20x from each side

50 + 1/20x -1/20x= 10 +1/15 x-1/20x

50 = 10 +1/15x - 1/20x

Subtract 10 from each side

40 = 1/15x - 1/20x

Get a common denominator

40 = 4/60x - 3/60x

40 =1/60x

Multiply by 60

40 *60 = 1/60x *60

2400 =x

Answer 2

Answer:

2400 pages

Step-by-step explanation:

First, let's make equations for the daily cost of the first printing press, with y being the total daily cost, and x being the total number of pages printed.

y=0.05x+50

Now, let's make an equation for the total daily cost of the second printing press.

y=(2/30)x+10

Since both equations are equal to y, let's use the substitution method and set them equal to each other.

0.05x+50=(2/30)x+10

Let's substitute 80 for x into both equations and see if we get a true statement.

0.05(80)+50=(2/30)(80)+10

4+50=16/3+10

54=46/3 X

Since this is a false statement, 80 pages cannot be the solution.

Now, let's try 1500 for x.

0.05(1500)+50=(2/30)(1500)+10

75+50=100+10

125=110 X

Since this is a false statement, 1500 pages cannot be the solution.

Now, let's try 2400 for x.

0.05(2400)+50=(2/30)(2400)+10

120+50=160+10

170=170

Since this is a true statement, 2400 pages is the correct solution, and it will lead to a daily cost of $170.