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.

Question

3c+2.5p = 31
c = 11−p
3c+2.5p
=
31

3(
)+2.5p
=
31

Answer 1

To substitute \( c = 11 - p \) into the first equation \( 3c + 2.5p = 31 \), we start with the first equation:

\[ 3c + 2.5p = 31 \]

Now, substitute \( c \) with \( 11 - p \):

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

Now, distribute \( 3 \) in the equation:

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

Combine like terms:

\[ 33 - 0.5p = 31 \]

Next, isolate \( p \) by first moving \( 33 \) to the right side:

\[ -0.5p = 31 - 33 \]

This simplifies to:

\[ -0.5p = -2 \]

Now, divide by \(-0.5\):

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

We have found \( p = 4 \). If you need the value of \( c \), substitute \( p \) back into \( c = 11 - p \):

\[ c = 11 - 4 = 7 \]

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