Iris charges a fee for her consulting services plus an hourly rate that is 11 times her fee. on a 7-hour job, iris charged $470. what is her fee 5 and her hourly rate?

To answer this question, we let x be the the consulting fee of Iris. With this representation, the value for the hourly rate is equal to 11x. The equation that would allow us to relate the consulting services fee, hourly fee and total value given that she worked for 7 hours would then be equal to,
      x + (7)(11x) = 470
Simplifying the left-hand side of the equation,
    78x = 470
Dividing the equation by 78 will give us an answer of 6. 

Hence,
  x = $6 (Consulting services fee)
 11x = 11($6) = $66 (hourly rate)