Question

You rewrote the second equation as c=11−p. You can now substitute c=11−p for c in the first equation to rewrite the first equation with one variable, p. Do that now.
3c+2.5p = 31
c = 11−p
3c+2.5p
=
31

3(
)+2.5p
=
31

Answer 1

To rewrite the first equation \(3c + 2.5p = 31\) with one variable using the expression for \(c\), we will substitute \(c = 11 - p\) into the first equation.

Starting with the first equation:

\[
3c + 2.5p = 31
\]

Substituting \(c\) with \(11 - p\):

\[
3(11 - p) + 2.5p = 31
\]

Now, distribute the 3:

\[
33 - 3p + 2.5p = 31
\]

Combine the \(p\) terms:

\[
33 - 0.5p = 31
\]

Now, you can isolate \(-0.5p\):

\[
-0.5p = 31 - 33
\]

This simplifies to:

\[
-0.5p = -2
\]

To solve for \(p\), divide both sides by \(-0.5\):

\[
p = \frac{-2}{-0.5} = 4
\]

So, \(p = 4\).

Now you can use this value of \(p\) to find \(c\) using \(c = 11 - p\):

\[
c = 11 - 4 = 7
\]

Thus, the solutions are \(p = 4\) and \(c = 7\).