18x-6y= 54 12y=6x-18 Solve this system of equations using the substitution method.
1 answer:
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Answer:
Salary of President = $180,000
Salary of Dept. Head = $60,000
Step-by-step explanation:
The question is to find the salary of president and department head.
We let the salary of one of department heads be "x"
Since, the salary of president is THREE (3) TIMES a department head, we can say:
Salary of President = 3x
Now, we know the total of these 2 salaries is 240,000. Thus, we can write:
Salary of President + Salary of Dept. Head = 240,000
3x + x = 240,000
Now, we can solve for x:
And now the president is "3x", so his salary is:
3(60,000) = 180,000
Thus,
President's salary = 180,000
Dept head's salary = 60,000
Correct so far. Finish up.
.. (x +3)(x)(x -1) = 1170
.. x^3 +2x^2 -3x -1170 = 0 . . . . . . one sign change ⇒ one positive real solution
This is a cubic equation with one positive real solution. There are several possible approaches to solving this. My favorite is to let a graphing calculator show me the solution.
You can also factor 1170 = 13*10*9, so x=10.
The width of the prism is 10 feet; the length is 13 feet; the height is 9 feet.
.. (x +3)(x)(x -1) = 1170
.. x^3 +2x^2 -3x -1170 = 0 . . . . . . one sign change ⇒ one positive real solution
This is a cubic equation with one positive real solution. There are several possible approaches to solving this. My favorite is to let a graphing calculator show me the solution.
You can also factor 1170 = 13*10*9, so x=10.
The width of the prism is 10 feet; the length is 13 feet; the height is 9 feet.