A math camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100. The camp can accomodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides, and * may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost

Using the minimum number of staff required for the camp to run properly, the number of aides and counsellors required to minimize cost is 18 and 12 respectively.

At minimum cost :

3 aides for every 2 counsellors gives a ratio of 3 : 2

Number of aides and counsellors to hire :

Aides = (3/5) × 30 = 18

Counsellors = 30 - 18 = 12

Therefore, to minimize cost, the number of aides and counsellors the camp may hire ls 18 and 12 respectively.

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They must hire 12 Counselors and 18 Aides

Step-by-step explanation: The most important factor here is the fact that they need to minimize hiring costs. The math camp can afford to hire up to 45 members of staff and can as well run properly with 30 members of staff.

The camp must have at least 10 aides (simply put, any number above 10 will do). Also they may have up to 3 aides for every 2 counselors, that is the ratio of counselor to aide has been given as;

2 : 3

If the math camp decides to hire the minimum required in order to minimize cost, they would be hiring 30, and that would be divided according to the following ratio;

(Counselor):

30 x 2/5 = 12

(Aide):

30 x 3/5 = 18

Hence they would be hiring 12 counselors at a cost of

2400 x 12 = 28800

And 18 Aides at a cost of

1100 x 18 = 19800

Therefore the total (minimum) cost of hiring staff is $48,600

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.