Question

At Gallicum Enterprises, all employees are in one of three categories: J, K, or L. The ratio of the numbers of employees in J to K to L has been 1:3:5 for some time. Last month, 20 new J employees were hired, and no employees left. If the new ratio of J to K is now 1:2 with these new J employees, what is the new total number of employees at Gallicum Enterprises

Answer 1

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

      $\frac{J}{K} = \frac{1}{3} \ (1)$

As last month, 20 new J employees were hired, new ratio of J to K is now

1 : 2.

So, $\frac{J+20}{K}=\frac{1}{2} \ (2)$

Dividing equation 1 and 2,

$\frac{J}{K}\div{\frac{J+20}{K} } = \frac{1}{3}\div{\frac{1}{2} }$

$\frac{J}{K}\times{\frac{K}{J+20} } = \frac{1}{3}\times{\frac{2}{1} }\\\\ \frac{J}{J+20} =\frac{2}{3}$

By cross multiplication:

$3J=2(J+20)\\3J=2J+40$

Subtracting both sides by $2J$

$J=40$

From equation 1.

$\frac{J}{K} = \frac{1}{3} \\\\ \frac{40}{K} =\frac{1}{3}$

By cross multiplication:

$K=40\times3\\\\ K=120$

As given, J : K : L = 1 : 3 : 5

So,  K : L =  3 : 5

  $\frac{K}{L} =\frac{3}{5} \\\\\\ \frac{120}{L} =\frac{3}{5}$

By cross multiplication:

$120\times5=3\times L\\600=3L$

Dividing both sides by 3

$L =200$

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.