When you see a function definition like
C(x) = 1.4x/(100-x)
the (x) after the C means that the variable in the function is named "x". To find a value for C, we need to put in some value for x.
When you are told that C=4, it means that
4 = 1.4x/(100-x)
You solve this in the usual way--undo what has been done to x. Several things have been done, so it takes several steps to undo them. We start by undoing the division by (100-x). To do that, we multiply both sides of the equation by (100-x)
4(100-x) = (100-x)1.4x/(100-x) = 1.4x
Now, we use the distributive property to undo the parentheses.
4*100 -4x = 1.4x
We can add 4x to both sides to put all the x terms together on one side of the equation.
400 = 4x + 1.4x = 5.4x
Now, we can divide by 5.4 so x is by itself. That is what we have been working toward.
400/5.4 = 5.4x/5.4 = x
We can perform the division by hand or using a calculator.
x = 400/5.4 ≈ 74.074
C(x) = 1.4x/(100-x)
the (x) after the C means that the variable in the function is named "x". To find a value for C, we need to put in some value for x.
When you are told that C=4, it means that
4 = 1.4x/(100-x)
You solve this in the usual way--undo what has been done to x. Several things have been done, so it takes several steps to undo them. We start by undoing the division by (100-x). To do that, we multiply both sides of the equation by (100-x)
4(100-x) = (100-x)1.4x/(100-x) = 1.4x
Now, we use the distributive property to undo the parentheses.
4*100 -4x = 1.4x
We can add 4x to both sides to put all the x terms together on one side of the equation.
400 = 4x + 1.4x = 5.4x
Now, we can divide by 5.4 so x is by itself. That is what we have been working toward.
400/5.4 = 5.4x/5.4 = x
We can perform the division by hand or using a calculator.
x = 400/5.4 ≈ 74.074
