Andrew earns $2 more than Barbara, who earned $30 more last week than Andrew. All amounts earned were at straight time. This is a number cross word puzzle mind bender homework problem. ? Andrews hourly rate and Barbara's hourly rate
Your first sentence doesn't make sense.
Let's solve this step-by-step.
Let's assume Andrew's hourly rate is $x.
According to the given information, Barbara earns $2 less than Andrew, so her hourly rate is $x - $2.
It is also given that last week, Barbara earned $30 more than Andrew.
So, we can set up the equation:
Barbara's earnings = Andrew's earnings + $30.
Since earnings are calculated based on the hourly rate and the number of hours worked, we can multiply the hourly rate by the number of hours worked to get the earnings.
Assuming both Andrew and Barbara worked the same number of hours, we can set up the equation:
(x - $2) * hours = x * hours + $30.
Now, let's solve this equation step-by-step to find the value of x (Andrew's hourly rate).
Expanding both sides of the equation:
x * hours - $2 * hours = x * hours + $30.
Canceling out the common term (x * hours):
-$2 * hours = $30.
Dividing both sides by the coefficient of hours (-$2):
hours = -$30 / -$2.
Simplifying the expression:
hours = $15.
Therefore, the number of hours worked by both Andrew and Barbara is 15.
Now, we can substitute the value of hours back into the equation to find the value of x (Andrew's hourly rate):
x * 15 - $2 * 15 = x * 15 + $30.
Simplifying the equation:
15x - $30 = 15x + $30.
Bringing like terms together:
15x - 15x = $30 + $30.
0 = $60.
Since we end up with an inconsistent equation (0 = $60), it means there is no solution.
So, based on the given information, we cannot determine the values of Andrew's or Barbara's hourly rates.
To find Andrew's hourly rate and Barbara's hourly rate, we need to set up equations based on the given information.
Let's assume Andrew's hourly rate is 'x' dollars per hour.
According to the given information, Andrew earns $2 more than Barbara. So, Barbara's hourly rate would be 'x - 2' dollars per hour.
Further, it is mentioned that Barbara earned $30 more last week than Andrew. We need to convert this into an equation.
If we multiply Andrew's hourly rate 'x' by the number of hours he worked last week, and Barbara's hourly rate 'x - 2' by the number of hours she worked last week, the difference between the two amounts would be $30.
Let's say Andrew worked 'h' hours and Barbara worked 'k' hours last week. The equation can be written as:
x * h - (x - 2) * k = 30
Simplifying the equation, we get:
xh - xk + 2k = 30
Now, we need additional information to solve this equation and find the exact values of x and k or h.