kofi wants to buy a new car, and he has narrowed his choicesto two models. Model

Question

kofi wants to buy a new car, and he has narrowed his choicesto two models. Model A sells for $15,500, gets 25 mi/gal, and costs $350 ayear for insurance Model B sells for $19,100, gets 48 mi/gal, and costs $425 ayear for insurance Kofi drives about 36000 miles a year, and gas costs about$4.50 a gallon. (a) Find a linear function A that models the cost A(x) ofowning Model A for x years. (b) Find a linear function B that models the cost B(x) ofowning Model B for x years. (c) Find the number of years of ownership for which the costto kofi of owning Model A equals the cost of owning Model b. kofi wants to buy a new car, and he has narrowed his choicesto two models. Model A sells for $15,500, gets 25 mi/gal, and costs $350 ayear for insurance Model B sells for $19,100, gets 48 mi/gal, and costs $425 ayear for insurance Kofi drives about 36000 miles a year, and gas costs about$4.50 a gallon. (a) Find a linear function A that models the cost A(x) ofowning Model A for x years. (b) Find a linear function B that models the cost B(x) ofowning Model B for x years. (c) Find the number of years of ownership for which the costto kofi of owning Model A equals the cost of owning Model b.

Explanation / Answer

x = each year Model A sells for $15,500, gets 25 mi/gal, and costs $350 ayear for insurance A = 15500 + 4.50(36000x/25) + 350x A = 15500 + 4.50(1440x) + 350x A = 15500 + 6480x + 350x a) A = 15500 +6830x Model B sells for $19,100, gets 48 mi/gal, and costs $425 ayear for insurance B = 19100 + 4.50(36000x/48) + 425x B = 19100 + 4.50(750x) + 425x B = 19100 + 3375x + 425x b) B = 19100 +3800x c) when will the cost of running each car beequal? when 15500 + 6830x = 19100 +3800x     subtract 3800x from each side of equation 15500 + 3030x = 19100   subtract 15500 from each side of equation 3030x = 3600 x=1.19 year at about 1 year 3 months thecars cost the same 3030x = 3600 x=1.19 year at about 1 year 3 months thecars cost the same

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