Use variables and set up equations.
\(3p + 4c = 40 \\ 5p + 2c = 34\)
Next, get one variable with equal coefficients.
\(3p + 4c = 40 \\ 10p + 4c = 68\ (multiplied\ both\ sides\ by\ 2)\)
Then get it alone on one side.
\(4c = 40-3p \\ 4c = 48-10p\)
Now we can use substitution. Since \(40-3p = 4c\), substitute \(40-3p\) for \(4c\) in the other equation and you'll get an equation with just one variable to simplify and solve.
\(40-3p = 68-10p \\ 40+7p = 68 \\ 7p = 28 \\ \boxed{p = 4}\)
We can then use \(p = 4\) in an earlier equation to find \(c\).
\(5p + 2c = 34 \\ 5*4 + 2c = 34 \\ 20 + 2c = 34 \\ 2c = 14 \\ \boxed{c=7}\)
