The cost of printing the first fifteen hundred copies of a book is $1500. It costs y dollars to print each subsequent copy. The cost of printing the first 7500 copies of the book is $7080. Find Y.
Please explain how to solve it.
just solve for y in:
1500 + (7500-1500)y = 7080
Y = 0.93
To solve this problem, we can set up a system of equations using the given information.
Let's denote the cost of printing the first fifteen hundred copies as C1 and the cost of printing each subsequent copy as y.
Similarly, we'll denote the cost of printing the first 7500 copies as C2.
From the information given, we have two equations:
Equation 1: C1 = 1500
This equation tells us that the cost of printing the first fifteen hundred copies is $1500.
Equation 2: C2 = 7080
This equation tells us that the cost of printing the first 7500 copies is $7080.
Now, we need to find the value of y, which represents the cost of printing each subsequent copy.
We can find the cost of printing the first 7500 copies by adding the cost of printing the first fifteen hundred copies (which is C1 = 1500) to the cost of printing the subsequent 6000 copies (which is 6000 * y).
So, the cost of printing the first 7500 copies (C2) can be expressed as:
C2 = C1 + (6000 * y)
7080 = 1500 + (6000 * y)
Next, let's solve this equation for y.
Subtract 1500 from both sides:
7080 - 1500 = 6000 * y
5580 = 6000 * y
Divide both sides by 6000:
5580 / 6000 = y
0.93 = y
Therefore, the value of y, which represents the cost of printing each subsequent copy, is $0.93.
To find the value of y, we need to set up an equation using the given information.
Let's denote the number of subsequent copies as x. From the given information, we know that the first 1500 copies cost $1500, so the cost per subsequent copy (y) can be expressed as:
1500 + xy = 1500y
Similarly, the cost of printing the first 7500 copies is $7080, so we can set up another equation:
7080 + xy = 7500y
Now we have a system of two equations:
1500 + xy = 1500y
7080 + xy = 7500y
To solve this system, we can subtract the first equation from the second equation:
(7080 + xy) - (1500 + xy) = 7500y - 1500y
Simplifying, we get:
5580 = 6000y
Dividing both sides by 6000, we find:
y = 5580 / 6000 = 0.93
Therefore, the value of y is $0.93.
To solve this problem algebraically, we set up a system of equations using the given information and then simplify and solve for the unknown variable (y).