a photocopy store advertises the following prices: 5 cents per copy for the first 20 copies, 4 cents per copy for the 21st through 100th copy, and 3 cents per copy after the 100th copy. Let x be the # of copies, and let y = the total cost of the photocopying. find the equation in the form y = mx+b that tells you the cost of making x copes when x is more than 100.
Sorry, the answer must be
y = 0.03x + 1.2
cost for 0 copy to 20 copy =$ 1
cost for 21 copy to 100 copy = 0.04*80 =$ 3.2
cost for 101 copy to 200 copy) = 0.03*100 =$ 3
then cost for 0 copy to 100 copy must be 4.2 dollars and the total cost for 200 copies must be 7.2 dollars.
thus =>
(y- 7.2)/(x-200) = (7.2-4.2)/(200-100)
(y- 7.2)/(x-200) = 0.03
(y- 7.2) = 0.03x - 6
y = 0.03x + 7.2 - 6
y = 0.03 + 1.2
Cost of 20 copies= 20x$0.05
=$1
Cost of 80 copies =80x0.04
=$3.20
Cost of 100 and more copies =0.03(x-100)
So our gradient. =0.03
Y=MX+b
Total cost =gradient x no of copies+ constant
4.20=0.03(100)+b
4.20=3+b
1.2=b
Y=0.03x+1.2
Thank you!
Well, well, well. It seems we have a math problem at hand. Let's see if I can help you solve it with a dash of humor.
So, for the first 20 copies, the price is 5 cents per copy. That means if your friend copies the entire Harry Potter series 20 times, it will cost them a whopping 100 cents! Quite a bargain, huh?
Now, here's where things get a bit interesting. For copies 21 to 100, the price drops down to 4 cents per copy. It's like a discount for all those procrastinators who wait until the last minute to make copies of their cat pictures, right? Anyway, back to the problem.
Once you exceed 100 copies, the price becomes a mere 3 cents per copy. It's like finding money in your old jeans pocket - you didn't expect it, but it's a pleasant surprise.
To find the equation in the form y = mx + b, we need to determine the slope (m) and y-intercept (b). Let's break it down.
For the copies beyond 100 (x > 100), the cost per copy is a fixed 3 cents. So our slope (m) will be 3. Easy peasy, lemon squeezy.
Now, for the y-intercept (b). Remember, for the first 20 copies, the price is 5 cents per copy. Therefore, when x = 20, the cost (y) will be 20 * 5 cents (or 100 cents). But we don't want the equation to include that, so we'll subtract it from the y-intercept.
So, our y-intercept (b) will be 100 - (20 * 5) cents.
Putting it all together, our equation becomes:
y = 3x + (100 - 20 * 5)
Simplifying it further:
y = 3x + (100 - 100)
And here's the final result:
y = 3x
Voila! The equation that tells you the cost of making x copies when x is more than 100 is simply y = 3x.
To find the equation in the form y = mx + b that tells you the cost of making x copies when x is more than 100, let's break down the pricing structure provided:
- First 20 copies: 5 cents per copy
- Copies 21-100: 4 cents per copy
- Copies exceeding 100: 3 cents per copy
We need to find the equation for the cost of making x copies when x is more than 100, so we'll only consider the pricing for copies exceeding 100.
Let's first determine the cost of making the first 100 copies. This can be found using the pricing structure given:
Cost of the first 20 copies = 20 * $0.05 = $1.00
Cost of the copies between 21 and 100 = 80 * $0.04 = $3.20
Therefore, the total cost of making the first 100 copies is $1.00 + $3.20 = $4.20.
For copies exceeding 100, we will need to find the cost per copy and add it to the total cost of the first 100 copies.
The cost per copy for copies exceeding 100 is 3 cents, which can also be written as $0.03.
Now, let's define the equation in the form y = mx + b:
y represents the total cost of photocopying
x represents the number of copies
Since we already know the total cost of making the first 100 copies is $4.20, we can set b (the y-intercept) to $4.20.
The cost per copy, m, when x is more than 100 is $0.03.
Therefore, the equation that tells you the cost of making x copies when x is more than 100 is:
y = 0.03x + 4.20
20 for 1.00
then 4*.80 = 3.20 for 21 through 100
so
4.20 for 100
y = 4.20 + .03 (x-100)
y = .03 x - 1.20