# Robert sells 3 packages of cookie dough and 8 packages of pie dough for $35. Phil sells 6 packages of cookie dough and 6 packages of pie dough for$45. How much does each type of dough cost?

May 21, 2017

Cookie dough: $5 Pie dough: $2.5

#### Explanation:

Just for shorting will call the cookie dough $\left(x\right)$ and the pie dough $\left(y\right)$.

We know Robert sold $3 x + 8 y$ for 35, and Phil sold $6 x + 6 y$ for 45.
To try to get to how much each cost, we need to put aside one of 'dough'; we do so by making one of the doughs even and then eliminate it (for now)

$\left(3 x + 8 y = 35\right) \text{ } \times \left(- 2\right)$

And if we put them together and subtract one by one,

$- 6 x - 16 y = - 70$

$6 x + 6 y = 45$

We get

$\left(- 10 y = - 25\right) \text{ } : \left(- 10\right)$

$y = 2.5$

Now we can return to the dough we left aside. And this time we already know how much pie dough cost so we put this, in case of Phil $6 \times 2.5 = 15$

And we left with this

$\left(6 x + 15 = 45\right) - 15$

$\left(6 x = 30\right) \text{ } : 6$

$x = 5$