Answer:
380.
Step-by-step explanation:
Given:
Total number of employees at Gallicum Enterprises are in the ratio,
J : k : L = 1 : 3 : 5 for some time.
Last month, 20 new J employees were hired, and no employees left and the new ratio of J to K is now 1 : 2.
Question asked:
What is the new total number of employees at Gallicum Enterprises ?
Solution:
<u>As given, J : K : L = 1 : 3 : 5 </u>
<em><u>So, J : K = 1 : 3 </u></em>
As last month, 20 new J employees were hired, new ratio of J to K is now
1 : 2.
So, ![\frac{J+20}{K}=\frac{1}{2} \ (2)](https://tex.z-dn.net/?f=%5Cfrac%7BJ%2B20%7D%7BK%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%20%5C%20%282%29)
Dividing equation 1 and 2,
![\frac{J}{K}\div{\frac{J+20}{K} } = \frac{1}{3}\div{\frac{1}{2} }](https://tex.z-dn.net/?f=%5Cfrac%7BJ%7D%7BK%7D%5Cdiv%7B%5Cfrac%7BJ%2B20%7D%7BK%7D%20%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cdiv%7B%5Cfrac%7B1%7D%7B2%7D%20%7D)
![\frac{J}{K}\times{\frac{K}{J+20} } = \frac{1}{3}\times{\frac{2}{1} }\\\\ \frac{J}{J+20} =\frac{2}{3} \\\\](https://tex.z-dn.net/?f=%5Cfrac%7BJ%7D%7BK%7D%5Ctimes%7B%5Cfrac%7BK%7D%7BJ%2B20%7D%20%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Ctimes%7B%5Cfrac%7B2%7D%7B1%7D%20%7D%5C%5C%5C%5C%20%5Cfrac%7BJ%7D%7BJ%2B20%7D%20%3D%5Cfrac%7B2%7D%7B3%7D%20%5C%5C%5C%5C)
By cross multiplication:
![3J=2(J+20)\\3J=2J+40](https://tex.z-dn.net/?f=3J%3D2%28J%2B20%29%5C%5C3J%3D2J%2B40)
Subtracting both sides by ![2J](https://tex.z-dn.net/?f=2J)
![J=40](https://tex.z-dn.net/?f=J%3D40)
From equation 1.
![\frac{J}{K} = \frac{1}{3} \\\\ \frac{40}{K} =\frac{1}{3} \\\\](https://tex.z-dn.net/?f=%5Cfrac%7BJ%7D%7BK%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%20%20%20%5C%5C%5C%5C%20%5Cfrac%7B40%7D%7BK%7D%20%3D%5Cfrac%7B1%7D%7B3%7D%20%20%5C%5C%5C%5C)
By cross multiplication:
![K=40\times3\\\\ K=120](https://tex.z-dn.net/?f=K%3D40%5Ctimes3%5C%5C%5C%5C%20K%3D120)
As given, J : K : L = 1 : 3 : 5
So, K : L = 3 : 5
![\frac{K}{L} =\frac{3}{5} \\\\\\ \frac{120}{L} =\frac{3}{5}](https://tex.z-dn.net/?f=%5Cfrac%7BK%7D%7BL%7D%20%3D%5Cfrac%7B3%7D%7B5%7D%20%5C%5C%5C%5C%5C%5C%20%5Cfrac%7B120%7D%7BL%7D%20%3D%5Cfrac%7B3%7D%7B5%7D)
By cross multiplication:
![120\times5=3\times L\\600=3L](https://tex.z-dn.net/?f=120%5Ctimes5%3D3%5Ctimes%20L%5C%5C600%3D3L)
Dividing both sides by 3
![L =200](https://tex.z-dn.net/?f=L%20%3D200)
<em>New total number of employees after hiring 20 new J employees :</em>
New J + K + L<u> =</u> (New J = J + 20 = 40 + 20 = 60 )
60 + 120 + 200 = 380
Therefore, the new total number of employees at Gallicum Enterprises is 380.