Question

A press received an order for printing 810 cards. Another press has to print 900 cards in

the same period of time. The first press completed its task 3 days after the target date and

the second, 6 days before the target date. How many cards did each press print per day, if

the second press made 5 more cards per day than the first?​

Answer 1

Step-by-step explanation:

Let the first press made x cards per day.

Then the second press made (x + 5) cards per day.

Let the time period given be y days.

Condition 1. The first press completed the task of printing 810 cards 3 after the target date.

Thus, it took (y + 3) days.

According to the question,

x (y + 3) = 810 . . . (i)

Condition 2. The second press completed the task of printing 900 cards 6 days before the target date.

Thus, it took (y - 6) days.

According to the question,

(x + 5) (y - 6) = 900 . . . (ii)

From (i), we get

y + 3 = 810/x

⇒ y = 810/x - 3

Putting y = 810/(x - 3) in (ii), we get

(x + 5) (810/x - 3 - 6) = 900

⇒ (x + 5) (810/x - 9) = 900

⇒ (x + 5) (810 - 9x)/x = 900

⇒ (x + 5) × 9 (90 - x)/x = 9 × 100

⇒ (x + 5) (90 - x) = 100x

⇒ 90x - x² + 450 - 5x = 100x

⇒ x² + 15x - 450 = 0

⇒ (x + 30) (x - 15) = 0

∴either x + 30 = 0 or, x - 15 = 0

⇒ x = - 30 or, x = 15

Since the number of productions cannot be negative, the exact value of x is 15.

Answer:

The first press made 15 cards per day and the second press made (15 + 5) = 20 cards per day.