# Question #eb036

Mar 11, 2017

We have 2 pieces of information that will give a pair of simultaneous equations to solve. First, take c to be the number of chocolate cookies and take r to be the number of raisin cookies.

We are told that the total number of cookies made is 168, so it will follow that:

$c + r = 168$

We are also told that there are 22 more chocolate cookies so their difference is 22:

$c - r = 22$

To use substitution, rearrange the 2nd equation to get c on one side:

$c = 22 + r$

Now we can replace $c$ in the top equation with this to get:

$\left(22 + r\right) + r = 168$

Rearrange this to obtain $r$ the number of raisin cookies:

$22 + 2 r = 168 \to 2 r = 168 - 22 = 146$

$\therefore 2 r = 146 \to r = \frac{146}{2} = 73$

So there are 73 raisin cookies. Now going back to the simultaneous equations, we now have a value for $r$ that can be substituted into the 2nd equation to get:

$c - r = 22$
$c - 73 = 22 \to c = 22 + 73 = 95$

Mar 11, 2017

Let $c =$ number of chocolate chip cookies, and
$r =$ number of oatmeal raisin cookies.

#### Explanation:

Then we know two things:
(1) $c + r = 168$ total number
(2) $c = r + 22$ difference between the two kinds

Substituton
We may now replace (substitute) the number $c = r + 22$ in the first equation:
$\left(r + 22\right) + r = 168$ take the $r$'s together:
$2 r + 22 = 168$ now subtract $22$ on both sides:
$2 r + \cancel{22} - \cancel{22} = 168 - 22$
$2 r = 146 \to r = 146 / 2 = 73$

Conclusion:
So he made $73$ oatmeal raisin cookies.
And $73 + 22 = 95$ chocolate chip cookies.

$73 + 95 = 168$. Check!