I broke it down to:
p(q) = 300
(p-5)(q+2n)=300
(p+5)(q-n)=300

then i just tested the answers, got to q=20, which worked. There must be a faster way, right? This seemed kinda time consuming.

guerrero wrote:A store sells a certain product at a fixed price per unit. At the product's current price, q units cost a total of exactly $300. If the price were lowered by $5 from its current value, then q + 2n units would cost exactly $300; if the price were raised by $5, then q - n units would cost exactly $300. What is the value of q?

A. 10
B. 15
C. 20
D. 25
E. 30

Need some help to tackle this question.

OA C

We need 3 prices spaced $5 apart that each divide into 300.
Make a list of options:
5, 10, 15, 20, 25, 30...

The prices above imply that the following numbers of units can be purchased:
300/5 = 60.
300/10 = 30.
300/15 = 20.
300/20 = 15.
300/25 = 12.
300/30 = 10.

According to the problem, the numbers of units that can be purchased are -- in ascending order -- q-n, q, and q+2n.
The difference between the greatest number and the median number (2n) is TWICE the difference between the median number and the least number (n).
Only the values in red satisfy this constraint:
30-20 = 10.
20-15 = 5.

Thus, the value of q -- the median number of units that can be purchased -- is 20.

The correct answer is C.