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 ellens dishwasher?

a. $1,030.44
b. $686.40
c. $1,093.73
d. $749.69

Question

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 ellens dishwasher?

a. $1,030.44
b. $686.40
c. $1,093.73
d. $749.69

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Sales Tax Calculation", "Operating Cost Analysis", "Lifetime Cost Calculation" ], "new_concepts": [], "current_concepts": [ "Sales Tax Calculation", "Operating Cost Analysis", "Lifetime Cost Calculation" ] } ## Calculate the total purchase price with sales tax Using the *Sales Tax Calculation* knowledge point $$ \begin{aligned} \text{Purchase Price} &= \$315 \times (1 + 0.0922) \ &= \$315 \times 1.0922 \ &= \$344.043 \ &\approx \$344.04 \end{aligned} $$ ## Determine the total number of uses over six years Using the *Operating Cost Analysis* knowledge point $$ \begin{aligned} \text{Total Weeks} &= 6 \text{ years} \times 52 \text{ weeks/year} = 312 \text{ weeks} \ \text{Total Uses} &= 312 \text{ weeks} \times 10 \text{ times/week} = 3,120 \text{ times} \end{aligned} $$ ## Calculate the total operating cost Using the *Operating Cost Analysis* knowledge point $$ \begin{aligned} \text{Cost per Use} &= \$0.09 \text{ (water)} + \$0.13 \text{ (electricity)} = \$0.22 \ \text{Total Operating Cost} &= 3,120 \text{ uses} \times \$0.22/\text{use} = \$686.40 \end{aligned} $$ ## Calculate the lifetime cost of the dishwasher Using the *Lifetime Cost Calculation* knowledge point $$ \begin{aligned} \text{Lifetime Cost} &= \text{Purchase Price} + \text{Total Operating Cost} \ &= \$344.043 + \$686.40 \ &= \$1,030.443 \ &\approx \$1,030.44 \end{aligned} $$

a. $1,030.44

b. $686.40

c. $1,093.73

d. $749.69

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Lifetime Cost Calculation" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the total purchase price with sales tax

Determine the total number of uses over six years

Calculate the total operating cost

Calculate the lifetime cost of the dishwasher

Answer: