Question

Iris charges a fee for her consulting services plus an hourly rate that is 1 1/5 times her fee. On a 7-hour, Iris charged $470. What is her fee and her hourly rate?

Answer 1

let's say she charges "x" for her consulting services.

so. she charges then for every hour 1 1/5x.  First let's convert that mixed fraction to "improper" and check what is "x".  Bearing in mind that, the 470 is for 7 hours of work, but the hourly rate only applies to the 1 1/5x, NOT the fixed consulting fee rate.

$\bf x+7\left( 1\frac{1}{5}x \right)=470\implies x+7\left( \cfrac{1\cdot 5+1}{5}x \right)=470 \\\\\\ x+7\left( \cfrac{6}{5}x \right)=470\implies x+\cfrac{42x}{5}=470\implies \cfrac{5x+42x}{5}=470 \\\\\\ 5x+42x=2350\implies 47x=2350\implies x=\cfrac{2350}{47}\implies \boxed{x=50}$

what's her hourly rate? well (6/5)x

Answer 2

F = Fee
F + 7(11/5)F = 470
5F + 77F = 2350
F = $28.66
Hourly rate is $63.05  
I've rounded up so this may not be exact.