Question

A bookstore can purchase several calculators for a total cost of $350. If each calculator cost $2 less, the bookstore could purchase 20 additional calculators at the same total cost. How many calculators can be purchased at the regular price?

Answer 1

x=cost of calculator
y=number of calculators

350=(x-2)*(20+y) <-- equation 1

we know that

total cost = cost per calc * number of calc bought

350 = x*y
so
350/y = x <-- equation 2

we can substitute x from equation 2 into equation 1

350=((350/y)-2)*(20+y)

solving this you get:
y^2+20y = 3500

by completing the square, add 100 to each side:
y^2+20y+100 = 3600

factoring this gives:
(y^2+10)(y^2+10)=3600

y^2+10 = 3600
y = 59.91

which rounds to 60 calculators

Answer 2

Sorry, made an error.

once you complete the square:
(y+10)^2 = 3600

solving for y gives you 50

so 50 calculators.

you could also used the quadratic formula to solve for y and get the same answer.