Acopy center offers its customers two different pricing plans for black and white photocopies of 8.5 in. by 11 in. pages. customers can either pay $0.08 per page or pay $7.50 for a discount card that lowers the cost to $0.05 per page. write and solve an equation to find the number of photocopies for which the cost of each plan is the same.

a) .08c .05c - 7.50; c = 250

b) . 05c .08c + 7.50; c = 22.5

c) 7.50 = .08c + 05c; c = 58

d) .08c = .05c + 7.50; c = 250

Writting the equation and solving it, the answer is option D) .08c = .05c + 7.50; c = 250

Solution:

If the number of photocopies is c

Plan 1: Customers can pay $0.08 per page

The cost with plan 1 is: C1=0.08c

Plan 2: Customers can pay $7.50 for a discount card that lowers the cost to $0.05 per page.

The cost with plan 2 is: C2=7.50+0.05c

We want to find the number of photocopies for which the cost of each plan is the same, then we equal the cost of each plan:

C1=C2

Replacing C1 by 0.08c and C2 by 7.50+0.05c

0.08c=7.50+0.05c

Solving this equation for c: Subtracting 0.05c both sides of the equation:

0.08c-0.05c=7.50+0.05c-0.05c

Subtracting:

0.03c=7.50

Dividing both sides of the equation by 0.03

0.03c/0.03=7.50/0.03

c=250

the one that has a slope of 1/2 and is positive.

step-by-step explanation: 2 buckets 1 trip ; 4 buckets 2 trips and so on.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.