A construction company employs technicians and artisans. One a certain day 4 technicians and artisans were hired and paid a total of sh 9000. On another day the firm hired 4 technicians and 1 artisans and paid a total of sh 9500. Calculate the cost of hiring 2 technicians and 5 artisans in a day.
daily rate of technician --- x
daily rate of artisan ---- y
"4 technicians and 1 artisans and paid a total of sh 9500"
---> 4x + y = 9500
"One a certain day 4 technicians and artisans were hired and paid a total of sh 9000" , could be
3x + y = 9000, y = 9000-3x ----- case1
2x + 2y = 9000 , y = 4500 - x , -- case2
x + 3y = 9000, x = 9000-3y, ---- case3
case1: 4x + (9000-3x) = 9500
x = 500, then y = 7500 , so 2x+5y = $38,500
case2: 4x + (4500-x) = 9500
x = 1666.67, y = 283.33, and 2x+5y = $17,500
case3: 4(9000-3y) +y = 9500
36000 - 12y + y = 9500
y = 2409.09 , x = 1772.73, and 2x+5y = $15,590.91
3x + 2y = 9000
4x + y = 9500
y = 9500 - 4x
3x + 2(9500 - 4x) = 9000
3x + 19000 - 8x = 9000
-5x = - 10000
x = 2000
y = 9500 - 8000
y = 1500
To calculate the cost of hiring 2 technicians and 5 artisans in a day, we need to determine the cost per technician and artisan.
Let's assume the cost per technician is represented by 'T' and the cost per artisan is represented by 'A'.
From the given information, we know that:
On the first day, 4 technicians and artisans were hired and paid a total of sh 9000. This can be written as equation (1): 4T + 4A = 9000.
On the second day, 4 technicians and 1 artisan were hired and paid a total of sh 9500. This can be written as equation (2): 4T + 1A = 9500.
Now, we can solve these two equations simultaneously to find the values of T and A.
Multiplying equation (2) by 4, we get: 16T + 4A = 38000.
Now, if we subtract equation (1) from equation (2) (or equivalently, add equation (1) with the negative of equation (2)), we get:
16T + 4A - 4T - 4A = 38000 - 9000,
12T = 29000.
Dividing both sides by 12, we find: T = 29000 / 12 = sh 2416.67.
Substituting the value of T in equation (1), we have:
4 * 2416.67 + 4A = 9000,
9666.68 + 4A = 9000,
4A = 9000 - 9666.68,
4A = -666.68.
Dividing both sides by 4, we get: A = -666.68 / 4 = -sh 166.67.
The negative result for A indicates an error in the given information since the cost cannot be negative.
Therefore, it is not possible to calculate the cost of hiring 2 technicians and 5 artisans with the current information provided.