Determine the amounts of 20% and 50% salt solutions that should be mixed to obtain 300 gallons of 41% salt solution.
1 answer:
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Simplifying
36c2 + -84cd + 49d2 = 0
Reorder the terms:
-84cd + 36c2 + 49d2 = 0
Solving
-84cd + 36c2 + 49d2 = 0
Solving for variable 'c'.
Factor a trinomial.
(6c + -7d)(6c + -7d) = 0
Subproblem 1
Set the factor '(6c + -7d)' equal to zero and attempt to solve:
Simplifying
6c + -7d = 0
Solving
6c + -7d = 0
Move all terms containing c to the left, all other terms to the right.
Add '7d' to each side of the equation.
6c + -7d + 7d = 0 + 7d
Combine like terms: -7d + 7d = 0
6c + 0 = 0 + 7d
6c = 0 + 7d
Remove the zero:
6c = 7d
Divide each side by '6'.
c = 1.166666667d
Simplifying
c = 1.166666667d
Subproblem 2
Set the factor '(6c + -7d)' equal to zero and attempt to solve:
Simplifying
6c + -7d = 0
Solving
6c + -7d = 0
Move all terms containing c to the left, all other terms to the right.
Add '7d' to each side of the equation.
6c + -7d + 7d = 0 + 7d
Combine like terms: -7d + 7d = 0
6c + 0 = 0 + 7d
6c = 0 + 7d
Remove the zero:
6c = 7d
Divide each side by '6'.
c = 1.166666667d
Simplifying
c = 1.166666667d
Solution
c = {1.166666667d, 1.166666667d}
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