Question #eb036

2 Answers
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:

#(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.

Mar 11, 2017

Answer:

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!