Two sociologists have grant money to study school busing in a particular city. they wish to conduct an opinion survey using 687 telephone contacts and 484 house contacts. survey company a has personnel to do 31 telephone and 11 house contacts per hour; survey company b can handle 22 telephone and 16 house contacts per hour. how many hours should be scheduled for each firm to produce exactly the number of contacts needed?

Company A should have 1.35 hours scheduled and company B 29.3 hours scheduled.

Step-by-step explanation:

This problem can be solved by a system of equations

I am going to say that x is the number of hours that company A should schedule and y is the number of hours that company B should schedule

We with to handle 687 telephone contacts. Company A can do 31 telephone contacts per hour, and company B can handle 22 telephone contacts per hour.

So

We with to handle 484 house contacts. Company A can do 11 house contacts per hour, and company B can handle 16 house contacts per hour.

So

So, we have to solve the following system of equations:

I am going to write y as a function of x in 1), and replace in 2)

Replacing

Multiplying everything by 22, we have

Company A should have 1.35 hours scheduled and company B 29.3 hours scheduled.

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x