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:
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:
It has been given that Becky earns 15% on sales over 1500, as commission, thus we have:
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