Question

Question #eb036

Answer 1

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:

`(22+r)+r=168`

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

`22 +2r=168 -> 2r = 168-22=146`

`therefore 2r= 146 -> r=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-> c=22+73=95`

Hence there 95 chocolate cookies and 73 raisin cookies.

Answer 2

Define your variables:
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:
`(r+22)+r=168` take the `r`'s together:
`2r+22=168` now subtract `22` on both sides:
`2r+cancel22-cancel22=168-22`
`2r=146->r=146//2=73`

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

Check your result:
`73+95=168`. Check!