To solve the equation: 1/4x + 2/5(104-x) = 32
First, distribute the 2/5 to the terms inside the parentheses:
1/4x + 2/5 * 104 - 2/5x = 32
Multiply 2/5 by 104:
1/4x + (2/5 * 104) - 2/5x = 32
1/4x + 208/5 - 2/5x = 32
Next, combine like terms:
(1/4 - 2/5)x + 208/5 = 32
To find a common denominator for 1/4 and 2/5, we multiply the denominators together (4 * 5 = 20):
(5/20 - 8/20)x + 208/5 = 32
Simplify the equation:
(-3/20)x + 208/5 = 32
Multiply both sides of the equation by the common denominator (20) to eliminate the fraction:
20 * (-3/20)x + (20 * 208/5) = 20 * 32
-3x + 416 = 640
Subtract 416 from both sides:
-3x = 224
Divide both sides by -3 to solve for x:
x = -224/3 or x = -74.67 (rounded to two decimal places)
Therefore, the solution to the equation is x = -74.67.
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