still inequalities

[demoskopico]

Laura sells encyclopedias, adn her monthtly income has 2 components, a fixed component of 1000$ per month , and a variable component, which is $C for each set of encyclopedias that she sells in that month over a sales target of n sets, where n>0. How much did she earn in March?

1. If Laura had sold 3 fewer sets in March, her income for that month would have been $600 lower than it was.
2.If Laura had sold 10 sets of encyclopaedias in March, her income for that month would have been over $4000.

please give me a very slow explanation, so that I can catch every passage

[kevin]

Laura's income for March on sales of x sets was $1000 + C(x - n) if x>n and 1000 otherwise

(1) By selling 3 fewer sets, Laura would have earned 600 less money. What is 600 in terms of C? It depends on where x is in relation to n. If x=n+1, she would have lost C (from 1000+C to 1000). If x=n+2, she would have lost 2C. If x > n+2, she would have lost 3C.

Thus 600 is either C, 2C, or 3C. We don't know which, so more information is needed

(2) 1000 +C(10 - n) > 4000, so C > 3000/(10-n) > 300/10= 300. This is not sufficient, either.

(T) (1) tells us that C is either 200, 300, or 600. (2) tells us that C must be greater than 300, so we know that C=600 and thus she sold one more than n. We can calculate her income for March: 1000 + C(1) = 1600. SUFF