Two sociologists have grant money to study school bussing pa

Two sociologists have grant money to study school bussing particular city. They wish to conduct an opinion survey using 600 telephone contacts and 400 house contacts. Survey company A personnel to do 30 telephone contacts and 10 house contacts per hour. Survey company B handle 20 telephone contacts and 20 house contacts per hour. How many hours should be scheduled for each survey company to produce exactly the number of contacts needed? set up the system of equations and solve it using Gauss-Elimination!

Solution

Number of contacts needed = 600 telephone (t) and 400 house (h) ;
company A per hour is : 30 t + 10 h
company B per hour is: 20 t + 20 h
Hence A( 30t + 10h ) + B (20 t + 20 h ) = 600 t + 400 h
(30 A + 20 B ) * t + (10A + 20B) * h = 600 t + 400 h
comparing coefficients of \'t\' and \'h\' we get:
30 A + 20 B = 600
10 A + 20 B = 400
subtracting them we get :
20 A = 200 so A = 10;
If A = 10 then 20B = 400 - 10*10 = 400-100 = 300
B = 300/20 = 15;

Hence number of hours of survey company A is 10 and of survey company B is 15;