A company sells cardboard that is nine and one-eighth millimeters thick. Write an equation to solve for the number of sheets of cardboard, c, in a pile that is two hundred fifty-five and one-half millimeters thick. What must be done to both sides to solve the equation?
9.125c = 255.5
Divide both sides of the equation by 9.125
To solve this problem, we can set up a proportion to find the number of sheets of cardboard, c, in a pile that is two hundred fifty-five and one-half millimeters thick.
Let's assume that x is the number of sheets required to reach a thickness of two hundred fifty-five and one-half millimeters.
The proportion can be written as:
9 and 1/8 millimeters / 1 sheet = 255 and 1/2 millimeters / x sheets
To solve the equation, we can cross-multiply:
(9 and 1/8) * x = (255 and 1/2) * 1
To simplify, we convert the mixed numbers into improper fractions:
(73/8) * x = (511/2) * 1
The next step is to remove the denominator by multiplying both sides of the equation by 8:
8 * (73/8) * x = 8 * (511/2) * 1
The 8 in the numerator and denominator cancel out on the left side, and the equation becomes:
73 * x = 8 * 511/2
To find the value of x, we divide both sides by 73:
x = (8 * 511/2)/73
To simplify, we can calculate the value on the right side of the equation:
x = 4096/146
Now, to find the final value of x, we divide the numerator by the denominator:
x ≈ 28
Therefore, the number of sheets required to reach a thickness of two hundred fifty-five and one-half millimeters is approximately 28.
To solve the equation, we multiplied both sides by 8, then divided both sides by 73.