Mark wants to buy some used CDs from Hastings. He can get 6 CDs for $50.10 and 9 CDs for $75.15. Write the equation that can be used to find f(x), the amount he would pay at this rate if he bought x CDs.
Thanks in advance :)
find the rate r so that
r = 50.10/6 or 75.12/9 , they are the same
f(x) = rx
To find the equation that can be used to find f(x), the amount Mark would pay if he bought x CDs, we can set up a linear equation using the given information.
Let's denote the number of CDs as x and the amount Mark would pay as f(x).
From the given information, we know that Mark can get 6 CDs for $50.10, which can be expressed as the ratio:
6 CDs / $50.10
Similarly, Mark can get 9 CDs for $75.15, which can be expressed as the ratio:
9 CDs / $75.15
To find the cost per CD, we can divide the number of CDs by the amount paid for them:
Cost per CD in the first scenario = $50.10 / 6 CDs
Cost per CD in the second scenario = $75.15 / 9 CDs
Now, we have the cost per CD in terms of the number of CDs, but we want to find the amount Mark would pay f(x) if he bought x CDs.
Using the concept of proportions, we can set up the equation:
(cost per CD in the first scenario) = (cost per CD in the second scenario)
($50.10 / 6 CDs) = ($75.15 / 9 CDs)
Now, we can express the cost per CD in terms of x and f(x):
($50.10 / 6) = ($75.15 / 9)
To find f(x), we multiply both sides of the equation by x:
($50.10 / 6) * x = ($75.15 / 9) * x
Simplifying the equation will give us f(x):
f(x) = (0.835 * x) + (8.35 * x)
Therefore, the equation that can be used to find f(x), the amount Mark would pay if he bought x CDs, is:
f(x) = 0.835x + 8.35x