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