To solve the given equation [tex]\( 4p + 9f = 60 \)[/tex], we aim to express one variable in terms of the other. Let's follow the steps to solve for [tex]\( p \)[/tex] in terms of [tex]\( f \)[/tex]:
1. Isolate [tex]\( p \)[/tex]:
[tex]\[
4p + 9f = 60
\][/tex]
Subtract [tex]\( 9f \)[/tex] from both sides of the equation:
[tex]\[
4p = 60 - 9f
\][/tex]
Divide both sides by 4 to isolate [tex]\( p \)[/tex]:
[tex]\[
p = \frac{60 - 9f}{4}
\][/tex]
Simplifying, we get:
[tex]\[
p = 15 - \frac{9f}{4}
\][/tex]
This equation tells us that [tex]\( p \)[/tex] is dependent on the value of [tex]\( f \)[/tex].
2. Example Solution:
Let's choose an example value for [tex]\( f \)[/tex]. Suppose [tex]\( f = 5 \)[/tex]. Now we substitute [tex]\( f = 5 \)[/tex] into the expression for [tex]\( p \)[/tex]:
[tex]\[
p = 15 - \frac{9 \cdot 5}{4}
\][/tex]
Calculate the value inside the fraction:
[tex]\[
p = 15 - \frac{45}{4}
\][/tex]
Simplify the fraction:
[tex]\[
p = 15 - 11.25
\][/tex]
[tex]\[
p = 3.75
\][/tex]
So, when [tex]\( f = 5 \)[/tex], we find that [tex]\( p \)[/tex] equals [tex]\( \frac{15}{4} \)[/tex] or 3.75.
In summary, a solution to the equation [tex]\( 4p + 9f = 60 \)[/tex] provides a relationship between [tex]\( p \)[/tex] and [tex]\( f \)[/tex]. An example solution is:
[tex]\[
(f, p) = (5, \frac{15}{4})
\][/tex]
