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

1 answer

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 \(c = 7\).