Subjects algebra

Spark Plug Profit Da653E

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1. **State the problem:** Calculate the shop owner's profit on 8 spark plugs. 2. **Given data:** - Cost per spark plug to owner: $2.33 - Quantity: 8 spark plugs - Price charged for 1 set of 8 spark plugs: $31.84 - Sales tax: 5% on parts only 3. **Calculate total cost to owner:** $$\text{Total cost} = 8 \times 2.33 = 18.64$$ 4. **Calculate sales tax on parts:** Parts include spark plugs, wires, distributor cap, rotor. Sum of parts before tax: $$31.84 + 73.92 + 24.16 + 9.10 = 138.02$$ Calculate 5% sales tax on parts: $$\text{Sales tax} = 0.05 \times 138.02 = 6.901$$ 5. **Calculate total price charged for spark plugs including tax:** Since $31.84$ is price before tax for spark plugs, add tax proportionally: Proportion of spark plugs in parts: $$\frac{31.84}{138.02} \approx 0.2307$$ Tax on spark plugs: $$6.901 \times 0.2307 \approx 1.59$$ Total price charged for spark plugs including tax: $$31.84 + 1.59 = 33.43$$ 6. **Calculate profit:** $$\text{Profit} = \text{Price charged including tax} - \text{Cost to owner}$$ $$= 33.43 - 18.64 = 14.79$$ **Final answer:** The shop owner's profit on the spark plugs is $14.79$.