Hi, can anyone help me solve this DS question?

Question

A candle company determines that, for a certain specialty candle, the supply function is p = m1x + b1 and the demand function is p = m2x + b2 , where p is the price of each candle, x is the number of candles supplied or demanded, and m1 , m2 , b1 , and b2 are constants. At what value of x do the graphs of the supply function and demand function intersect? 
1. m1 = –m2 = 0.005 
2. b2 – b1 = 6

V Gupta · Accepted Answer

You're trying to find where the supply and demand curves intersect, so set both equations equal: m1 * x + b1 = m2 * x + b2 That simplifies to: (m1 &ndash; m2) * x = b2 &ndash; b1
Statement 1 gives m1 = &ndash;m2 = 0.005 &rarr; so m1 &ndash; m2 = 0.005 &ndash; (&ndash;0.005) = 0.01. Nice, we&rsquo;ve got the slope difference. But we still don&rsquo;t know b2 &ndash; b1, so x is unsolvable.
Statement 2 gives b2 &ndash; b1 = 6, but doesn&rsquo;t say anything about m1 or m2 &mdash; again, not enough to solve for x.
Put both together and now it works: x = 6 / 0.01 = 600
So yeah, both statements are needed. Answer is C.

Mansih K · Answer

Basically, you&rsquo;ve got two linear equations and need to find where they cross &mdash; so you just set them equal.
Statement 1 says m1 = &ndash;m2 = 0.005, which means m1 &ndash; m2 = 0.01. That gives the slope difference. But unless you know the b-values, you can&rsquo;t get x.
Statement 2 gives b2 &ndash; b1 = 6. That&rsquo;s helpful, but without the slope difference, you&rsquo;re still stuck.
Combine both and it&rsquo;s easy: x = (b2 &ndash; b1) / (m1 &ndash; m2) = 6 / 0.01 = 600
So neither works alone, but together they&rsquo;re enough. Definitely go with C.