Question 96702
Let x=number of types of cakes
Then x+6=number of types of cookies


Now we are told that:

x+x+6=32  subtract 6 from both sides

x+x+6-6=32-6  collect like terms
2x=26  divide both sides by 2

x=13---------------------number of types of cakes

x+6=13+6=19------------------number of types of cookies

CK
13+19=32
32=32

also 19 is 6 more than 13


Another way:

Let x=number of types of cakes
And y=number of types of cookies

Now we are told that x+y=32--------------------------eq1

We are also told that y=x+6--------------------------eq2

Rearrange eq2 by subtracting x from both sides and we get:

y-x=6--------------------------------eq2

Add eq1 and eq2:
2y=38  divide both sides by 2

y=19--------------------number of types of cookies

substitute y=19 into eq1
x+19=32  subtract 19 from both sides
x+19-19=32-19  collect like terms
x=13---------------------------------number of types of cakes

Hope this helps---ptaylor