Hi John!
You can set the problem up as follows:
x = number of apples pies
3x = the number of cherry pies ("three times as many cherry pies as apple")
x+7 = number of razzleberry pies ("seven more razzleberry pies than apple)
72 = total number of pies
Now we can set up an algebraic equation:
number of number of number of Total number
apple pies cherry pies razzleberry pies of pies
x + 3x + (x + 7) = 72
4x + (x + 7) = 72 ... next, solve for "x" by fist
5x + 7 = 72 combining all "x"s:
5x + 7 - 7 = 72 - 7 .... now subtract "7" from both sides
eliminate it from the right side
to further simplify the equation:
5x = 65
5x = 65 ... now divide both side by 5 to further
5 5 simplify the equation
x = 13 ... number of apple pies
Now we know the number of apple pies we can use the equations segments above to find the number of each of the other two types of pie
x = 13 - number of apple pies
3x = 3(13) = 39 - number of cherry pies
(x + 7) = (13 + 7) = 20 - number of razzleberry pies
To check our work, our three pie numbers immediately above should add up to 72. Let's see!
13 + 39 + 20 = 72
52 + 20 = 72
72 = 72
Yep! Our pie count is right!
