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
