Question

The startup department made 80% of 1/2 of the established department. The start up departments growth was 1/3 greater than the established departments . If the departments made $280,000 combined , how much did the start up department make

Answer 1

Answer:

The start up department make $80,000.

Step-by-step explanation:

Given:

The startup department made 80% of 1/2 of the established department. The start up departments growth was 1/3 greater than the established departments .

If the departments made $280,000 combined.

Now, to find the amount start up department make.

Let the amount of start up department be $x.$

And let the amount of established department be $y.$

As, the startup department made 80% of $\frac{1}{2}$ of the established department.

So, we put an equation:

$x=80\%\ of\ \frac{1}{2}\ of\ y\\\\x=\frac{80}{100} \times \frac{1}{2}\times y\\\\x=0.80\times \frac{y}{2} \\\\x=0.4y$

$x=0.4y\ \ \ ......(1)$

Now, the combined amount of both departments:

$x+y=280,000$

Substituting the value of $x$ from equation (1) we get:

$0.4y+y=280,000$

$1.4y=280,000$

Dividing both sides by 1.4 we get:

$y=200,000.$

Now, substituting the value of $y$ in equation (1) we get:

$x=0.4y\\\\x=0.4\times 200,000\\\\x=80,000.$

Thus, the amount of start up department make = $80,000.

Therefore, the start up department make $80,000.