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ours of overtime, and earned $784\$784. She is paid a olve the equation 40x+6(1.5x)=78440x+6(1.5x)=784 to find her (Simplify your answer.)

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Q. ours of overtime, and earned $784\$784. She is paid a olve the equation 40x+6(1.5x)=78440x+6(1.5x)=784 to find her (Simplify your answer.)
  1. Given Equation: We are given the equation 40x+6(1.5x)=78440x + 6(1.5x) = 784, where xx represents the hourly wage. The first term, 40x40x, represents the pay for the regular 4040 hours, and the second term, 6(1.5x)6(1.5x), represents the pay for 66 hours of overtime at a rate of 1.51.5 times the regular hourly wage.
  2. Simplify Equation: First, we simplify the equation by distributing the 1.51.5 into the 6x6x. \newline40x+6×1.5x=78440x + 6 \times 1.5x = 784\newline40x+9x=78440x + 9x = 784
  3. Combine Like Terms: Next, we combine like terms 40x40x and 9x9x to simplify the equation further.40x+9x=49x40x + 9x = 49x49x=78449x = 784
  4. Solve for x: Now, we solve for xx by dividing both sides of the equation by 4949.49x49=78449\frac{49x}{49} = \frac{784}{49}x=16x = 16
  5. Final Result: We have found the value of xx, which represents the hourly wage.x=16x = 16

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