Ellen purchased a dishwasher, which cost $315 before the 9.22% sales tax. she used the machine an average of 10 times per week for the next six years, at which point she replaced it. each time she ran the dishwasher it cost her $0.09 for water and $0.13 for electricity. what was the lifetime cost of ellen's dishwasher?

First let's get the cost of the dishwasher:  315 * 1.0922 = 344.04

This is the cost of the dishwasher $315 times the sales tax of 9.22 (expressed as 1.0922 in order to add it in to the total).

Then we have 52 weeks in a year.  52* 6 (number of years) is 312 weeks.  She used it 10x per week so its 312*10 = 3120

Each use costs .09 for water and .13 for electricity or .22 cents per use

So we take the total uses 3120 * .22 per use = 686.40

Add the use cost of 686.4 + 344.04 (Purchase with tax) = $1030.44 Lifetime cost