Suppose s is a set of 10 integers (any integers at all). prove that there are a pair of numbers in s whose difference is a multiple of 9; i. e. prove that there exists a, b ∈ s and an integer k ∈ z such that a − b = 9k. (hint: apply the pigeonhole principle to the potential remainders of elements of s with respect to division by 9).

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3