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

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

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.