Respuesta :
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:
As given, J : K : L = 1 : 3 : 5
So, J : K = 1 : 3
[tex]\frac{J}{K} = \frac{1}{3} \ (1)[/tex]
As last month, 20 new J employees were hired, new ratio of J to K is now
1 : 2.
So, [tex]\frac{J+20}{K}=\frac{1}{2} \ (2)[/tex]
Dividing equation 1 and 2,
[tex]\frac{J}{K}\div{\frac{J+20}{K} } = \frac{1}{3}\div{\frac{1}{2} }[/tex]
[tex]\frac{J}{K}\times{\frac{K}{J+20} } = \frac{1}{3}\times{\frac{2}{1} }\\\\ \frac{J}{J+20} =\frac{2}{3} \\\\[/tex]
By cross multiplication:
[tex]3J=2(J+20)\\3J=2J+40[/tex]
Subtracting both sides by [tex]2J[/tex]
[tex]J=40[/tex]
From equation 1.
[tex]\frac{J}{K} = \frac{1}{3} \\\\ \frac{40}{K} =\frac{1}{3} \\\\[/tex]
By cross multiplication:
[tex]K=40\times3\\\\ K=120[/tex]
As given, J : K : L = 1 : 3 : 5
So, K : L = 3 : 5
[tex]\frac{K}{L} =\frac{3}{5} \\\\\\ \frac{120}{L} =\frac{3}{5}[/tex]
By cross multiplication:
[tex]120\times5=3\times L\\600=3L[/tex]
Dividing both sides by 3
[tex]L =200[/tex]
New total number of employees after hiring 20 new J employees :
New J + K + L = (New J = J + 20 = 40 + 20 = 60 )
60 + 120 + 200 = 380
Therefore, the new total number of employees at Gallicum Enterprises is 380.
