Algebra equation

Question

Rose spent $2.40 on pens. If each pen had cost 4 cents more, she would have been able to buy 10 fewer pens for the same money. How many pens did rose buy ?

I'm having trouble writing this equation. They want me to write a fractional equation for this. Can you please help ?.

Answer 1

Let the number of pens be p and their cost in cents be c

Then,

pc = 240

(p-10)(c+4) = 240

Multiplying through the bottom expression

pc - 10c + 4p - 40 = 240

From the top expression, we know that c = 240/p

Substituting into the bottom expression, we have

p(240/p) - 10(240/p) + 4p - 40 = 240

240 - 2400/p + 4p - 40 = 240 -

4p - 2400/p - 40 = 0

Multiply through by p

4p^2 - 2400 - 40p = 0

4p^2 - 40p - 2400 = 0

Dividing by 4,

p^2 - 10p - 600 = 0

(p-30)(p + 20) = 0

p = 30, -20.

We can not have a negative price, so p = 30. As pc = 240, c = 240/30 = 8

To check, if the pen costs 4 cents more, it is 8+4 = 12. Then, we purchase 10 fewer = 30 - 10 = 20

20 * 12 = 240. It checks.