The organizers of of a walkathon get cost estimates from two printing companies to print brochures to advertise the event. The cost are given by the equations below, were C is the cost in dollars and N is the number of brochures.

Company A: C = 15 + 0.10n
Company B: C = 0.25n
A: for what number of brochures are the costs the same for both companies? What method did you use to get your answer? B: The organizers have 65$ to spend on brochures. How many brochures can they have printed if they used company A? If they use company B? C

A: To find the number of brochures for which the costs are the same for both companies, we need to set the two cost equations equal to each other and solve for N.

Company A: C = 15 + 0.10n
Company B: C = 0.25n

Setting them equal to each other:
15 + 0.10n = 0.25n

Subtracting 0.10n on both sides:
15 = 0.15n

Dividing both sides by 0.15:
n = 100

Therefore, the costs are the same for both companies when 100 brochures are printed.

B: To find the number of brochures the organizers can have printed with $65, we need to substitute the cost equation into the respective company's equation and solve for N.

Using Company A's cost equation:
C = 15 + 0.10n
65 = 15 + 0.10n

Subtracting 15 on both sides:
50 = 0.10n

Dividing both sides by 0.10:
n = 500

Therefore, the organizers can have 500 brochures printed if they use Company A.

Using Company B's cost equation:
C = 0.25n
65 = 0.25n

Dividing both sides by 0.25:
n = 260

Therefore, the organizers can have 260 brochures printed if they use Company B.

A: To find the number of brochures where the costs are the same for both companies, we need to set the two cost equations equal to each other and solve for N.

Setting the equations equal to each other:
15 + 0.10n = 0.25n

Subtracting 0.10n from both sides:
15 = 0.25n - 0.10n

Combining like terms:
15 = 0.15n

Dividing both sides by 0.15:
n = 100

Therefore, the costs will be the same for both companies when the number of brochures is 100.

To answer part B, we can plug in the given budget of $65 into the cost equations of both companies to find the maximum number of brochures they can print.

For company A:
C = 15 + 0.10n
65 = 15 + 0.10n
50 = 0.10n
n = 500

So, with a budget of $65, the organizers can have 500 brochures printed using company A.

For company B:
C = 0.25n
65 = 0.25n
n = 260

Therefore, with a budget of $65, the organizers can have 260 brochures printed using company B.