cost question 2

Question

The cost of printing name card is given by the equation y= k+3000/x. where y cents is the cost per card, x is the number if cards printed and k is a constant. Given that y= 10 when x= 600, (a) find the vlue of k    (b) using the value of k, calculate the cost per card if 750 cards are printed.   (c) how many cards will be printed if the cost is to be 7.5 cents ?

Answer 1

a. We substitute the given information in the equation to find k (y =10, x =600):

 y = k + 3000/x

10 = k + 3000/600

10 = k + 5

k = 10 -5

k =5.

Cost function is

y = 5 +3000/x

 

b. To find the cost per card, we let x =750 in the cost function:

then

y = 5 + 3000/750

y = 5 + 4

y = 9.

 

Cost per card is 9 cents.

 

c. Now, we know cost y is 7.5 cents, and solve for y.

7.5 = 5 + 3000/x

7.5 - 5 = 3000/x

2.5 = 3000/x

x = 3000/2.5

x = 1200.

 

We need to produce 1200 name cards for the cost to be 7.5 c.