Alex spent 35 dollars on cookies. If the cookies were 1 dollar cheaper, he would be able to buy 4 more cookies. How many cookies did alex buy? Reduce the problem to a quadratic equation in terms of c the number of cookies by eliminating p the price of a cookie.
Let p be the original price per cookie and c the number bought
So
cp = 35 ⇒ p = 35 / c
And
(c + 4)) ( p -1) = 35
(c + 4) ( 35/c - 1) = 35
35 + 140/c - c - 4 = 35
-c + 140/c + 31 = 35
-c + 140/c - 4 = 0 multipy through by -c
c^2 + 4c - 140 = 0 factor
(c + 14) ( c - 10) = 0
The second factor set to 0 and solved for c = 10
He originally bought 10 cookies and their cost was $3.50 each = $35
So 4 more at a $1 price reduction per coookie gives.......
14 (2.50) = $35