Question

At Lincoln Library there are two ways to pay for copying. You can pay 11 cents a copy, or you can buy a plastic card for $5 and then pay 6 cents a copy. Let x be the number of copies you make. Write an equation for your costs for each way of paying. (Express C(x) in dollars.) C(x) = without card C(x) = with card (a) How many copies do you need to make before buying the plastic card is the same as cash? copies (b) If you wish to make 95 copies, which way of paying has the least cost? O with card Othey are the same O cannot be determined without card

Answer 1

Answer:

Without card: C(x) = .11x

With card: C(x) = 5 + .06 x

a) 100 copies

b) Without card.

Step-by-step explanation:

If x is the number of copies you make and you don't have a card, it will cost you 11 cents per copy = .11x

C(x) = .11x

If you do have a card, each copy will cost you 6 cents, therefore it will cost you .06x plus the 5 dollars you paid for the card.

C(x) = 5 +.06x

a) How many copies do you need to make before buying the plastic card is the same as cash? We need both equations to be the same:

$.11x=5+.06x\\.11x-.06x=5\\.05x=5\\x=5/.05\\x=100$

Therefore we will need 100 copies.

b) If you wish to make 95 copies, which way of paying has the least cost?

Without card:

C(95) = .11(95) = 10.45

With card:

C(95) = 5 + .06(95) = 5 + 5.7 = 10.7

The least cost would come paying without card.