I can't figure this problem out, it is very confusing.

Question

A printing company charges $65 for 100 business cards and $140 for 225 business cards. When x is the number of business cards, what is the cost per business card?

Answer 1

It's a matter of converting the information given into equations: y = mx+ b. Doing that, here's what we know:

y = the final cost of the cards, and x = the number of cards produced (as the final cost is determined by the number of cards made)

65 = 100m + b (100 cards costs $65)

140 = 225m + b (225 cards costs $140)

Now, the equation is asking for how much each card costs. In other words, they want us to find m, the slope. to find the slope, we use the slope formula:

m = (y₂ - y₁) / (x₂ - x₁)

Thanks to our equation setup earlier, we know what our x and y values are going to be:

m = (140 - 65) / (225 - 100)

m = ⁷⁵ / ₁₂₅

Factoring out 25:

m = ^{25 * 3} / _{25 * 5}

m = ³/₅ = ⁶/₁₀ = 0.6

And so, each card costs $0.60 to produce.

Answer 2

Start with two-point form (should be in your text book

(y - 100) / (x - 65) = (225 - 100) / (140 - 65)

Now solve for y.