The amount of money a worker makes varies directly with the hourly rate of pay. Worker A earns $168 for an 8-hour period. Worker B earns the same hourly rate as Worker A but works for only 6 hours. What does Worker B earn?
Responses
A $1008$1008
B $126$126
C $1344$1344
D $160
Since the amount of money a worker makes varies directly with the hourly rate of pay, we can set up a proportion to solve for Worker B's earnings.
The proportion is $\frac{\text{Worker A's earnings}}{\text{Worker A's hours}} = \frac{\text{Worker B's earnings}}{\text{Worker B's hours}}$.
Substituting the given values, we have $\frac{168}{8} = \frac{\text{Worker B's earnings}}{6}$.
Cross-multiplying, we get $6 \cdot 168 = 8 \cdot \text{Worker B's earnings}$.
Simplifying, we have $1008 = 8 \cdot \text{Worker B's earnings}$.
Dividing both sides by 8, we find $\text{Worker B's earnings} = \boxed{126}$. Therefore, the answer is $\boxed{\text{(B)}}$
To find out how much Worker B earns, we can set up a proportion using the direct variation relationship between the amount of money a worker makes and the number of hours worked.
The proportion can be set up as follows:
Amount of money Worker A makes / Number of hours Worker A works = Amount of money Worker B makes / Number of hours Worker B works
We know that Worker A earns $168 for an 8-hour period. So, the proportion becomes:
$168 / 8 = Amount of money Worker B makes / 6
To solve for the amount of money Worker B makes, we can cross-multiply:
Amount of money Worker B makes = ($168 / 8) * 6
Simplifying the right side of the equation:
Amount of money Worker B makes = $21 * 6
Amount of money Worker B makes = $126
Therefore, Worker B earns $126.
The correct answer is B, $126.
To find out what Worker B earns, we need to determine the hourly rate of pay for both Workers A and B and then calculate Worker B's earnings based on the given information.
First, let's determine Worker A's hourly rate of pay. We know that Worker A earns $168 for an 8-hour period. To calculate the hourly rate, we divide the total earnings by the number of hours worked:
Hourly rate of pay for Worker A = $168 / 8 hours = $21 per hour
Worker B earns the same hourly rate as Worker A. So, Worker B's hourly rate of pay is also $21 per hour.
Now that we know the hourly rate, we can calculate Worker B's earnings. Worker B works for 6 hours, so we multiply the hourly rate of $21 by the number of hours worked:
Earnings for Worker B = $21 per hour * 6 hours = $126
Therefore, Worker B earns $126.
So, the answer is B: $126.