If Becky makes $3458.55 in a week, then we have to first obtain the commision she got from the the first 1500 she made out of the 3458.55.
It has been given that she's paid a commission of 5.40% of her first 1500 in sales, thus we have:
[tex]\begin{gathered} \frac{5.40}{100}\times1500 \\ =\text{ 81} \end{gathered}[/tex]Hence, Becky earns $81 in commission from the first 1500 in sales.
The amount left from the 3458.55 after earning commission on the first 1500 is:
[tex]3458.55-1500=1958.55[/tex]It has been given that Becky earns 15% on sales over 1500, as commission, thus we have:
[tex]\begin{gathered} \frac{15}{100}\times1958.55 \\ =293.78 \end{gathered}[/tex]Hence, Becky earns $293.78 in commission on the remaining amount made in sales.
Hence, her total commission in a week during which she sells 3458.55 worth of appliance is: 81 + 293.78 = $374.78