Let x represent the amount invested at 6% and y the amount at 9%.
The equation x+y=8,500 leads to x=8500-y.
For the interest rates, we know 6%=0.06 and 9%=0.09.
The equation becomes 0.06x + 0.09y=667.5 (substituting for x to use only y).
Expanding yields: 0.06(8500-y)+0.09y=667.5.
Solving this gives us 510-0.06y+0.09y=667.5 (-510).
This simplifies to 0.03y=117.5 (/0.03), yielding y=$3916.67 for the 9% investment.
Thus, X=8500-Y results in x=$4583.33 for the 6% investment.
X - 9 + 2wx = y Add 9 to both sides of the equation to isolate terms.
Next, you get x + 2wx = y + 9. After that, factor out x to obtain x (1 + 2w) = y + 9.
Lastly, divide every term by (1 + 2w) yielding x = (y + 9) / (1 + 2w).
Conclusion:
Please refer to the explanation provided.
Detailed explanation:
Starting with these facts:
Total revenue = $250
Fee charged = $70 per car
Tips received = $50
Equation 1 representing the above:
(Fee per car × number of cars) + tips = total revenue
Let the number of cars be c.
Thus, we have:
$70c + $50 = $250
Part B:
Total revenue = $250
Fee charged = $75 per car
Tips received = $35
Supplies cost per car washed = $5
Equation 2:
(Fee per car × number of cars) + tips - (supplies cost × number of cars) = total revenue
$75c + $35 - $5c = $250
$70c + $35 = $250
Part C:
Equation 1 does not factor in costs associated with washing the car, while equation 2 does incorporate costs, which are deducted from the amount charged per car. Additionally, tips in equation 1 total $50 compared to a $35 fee in equation 2.
Kevin, since the problem states a number (x) minus 20, and given that 20 is mentioned later, it indicates that it is the second number involved here.
Here, 'a' relates to 0.
There are two scenarios for 'r' and 't'.
Scenario 1.
Both are positioned on the same side to the right of 'a'.
In this case, 'r' would equal 5, and 't' would equal 7.
The midpoint between 'r' and 't' is 
.
Scenario 2.
If both are found to the left of 'a'.
Then 'r' would equal -5, while 't' would equal -7.
The midpoint is 
.
Scenario 3.
If 'r' is right of 'a' and 't' is left of 'a'.
Thus 'r' equals 5 and 't' equals -7.
The midpoint is 
.
Scenario 4.
If 'r' is left of 'a' while 't' is right of 'a'.
In this case, 'r' corresponds to -5 and 't' corresponds to 7.
The midpoint is 
.
The potential midpoint coordinates for 'rt' are 6, -6, 1, and -1.
