Problem Solving

swerve wrote:At a certain factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

Let's assign a "nice" value to the number of widgets made by ONE employee.
We'll also assign a nice value to the number of employees on each shift.

At a certain factory, each employee working the SECOND shift produced 2/3 as many widgets as each employee working the FIRST shift.
Let's say that EACH employee on the FIRST shift makes 3 widgets during the shift.
So, EACH employee on the SECOND shift makes 2 widgets during the shift.

The first shift has 3/4 as many employees,
Let's say that the SECOND shift has 4 employees
This means the FIRST shift has 3 employees

What fraction of the total widgets did the second shift produce?
The FIRST shift has 3 employees, and EACH employee makes 3 widgets for a TOTAL of 9 widgets
The SECOND shift has 4 employees, and EACH employee makes 2 widgets for a TOTAL of 8 widgets

So, altogether, the number of widgets made = 9 + 8 = 17
The SECOND shift made 8 widgets of the widgets, so the SECOND shift made 8/17 of the widgets.

Answer: A

Cheers,
Brent

swerve wrote:At a certain factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

The OA is A

Source: Veritas Prep

We can let the number of widgets produced by each employee in the first shift = 3 and the number of widgets produced by each employee in the second shift = 2.

We can let the number of employees in the second shift = 4 and the number in the first shift = 3.
The total widgets produced was (3 x 3) + (2 x 4) = 9 + 8 = 17.

So the fraction of widgets produced by the second shift was 8/17.

Answer: A