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.
[tex]\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}[/tex]
what's her hourly rate? well (6/5)x
