You currently drive $240$ miles per week in a car that gets $24$ miles per gallon of gas. You are considering buying a new fuel-efficient car for $\$ 13,000$ (after trade-in on your current car) that gets $40$ miles per gallon. Insurance premiums for the new and old car are $\$ 720$ and $\$ 500$ per year, respectively. You anticipate spending $\$ 1050$ per year on repairs for the old car and having no repairs on the new car. Assume gas costs $\$ 2.45$ per gallon. Over a seven-year period, is it less expensive to keep your old car or buy the new car? By how much? $\newline$ the new car is $\$ 3420.08$ less expensive $\newline$ the old car is $\$ 3622.80$ less expensive $\newline$ the new car is $\$ 3420.08$ less expensive $\newline$ the old car is $\$ 3622.80$ less expensive

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Algebra 2

Find probabilities using the addition rule

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Q. You currently drive

240

miles per week in a car that gets

24

miles per gallon of gas. You are considering buying a new fuel-efficient car for

\$ 13,000

(after trade-in on your current car) that gets

40

miles per gallon. Insurance premiums for the new and old car are

\$ 720

and

\$ 500

per year, respectively. You anticipate spending

\$ 1050

per year on repairs for the old car and having no repairs on the new car. Assume gas costs

\$ 2.45

per gallon. Over a seven-year period, is it less expensive to keep your old car or buy the new car? By how much?

\newline

the new car is

\$ 3420.08

less expensive

\newline

the old car is

\$ 3622.80

less expensive

\newline

the new car is

\$ 3420.08

less expensive

\newline

the old car is

\$ 3622.80

less expensive

Calculate total miles driven: Calculate the total miles driven in $7$ years: $240$ miles/week $\times$ $52$ weeks/year $\times$ $7$ years.
Calculate total gas used (old car): Total miles in $7$ years = $240 \times 52 \times 7 = 87360$ miles.
Calculate gas cost (old car): Calculate the total gallons of gas used by the old car: $87360$ miles / $24$ miles/gallon.
Calculate total gas used (new car): Total gallons for old car = $87360 / 24 = 3640$ gallons.
Calculate gas cost (new car): Calculate the total cost of gas for the old car: $3640 \text{ gallons} * (\$2.45/\text{gallon})$ .
Calculate insurance cost (old car): Total gas cost for old car = $$3640$ \times $2$.$45$ = \$($8922$).
Calculate insurance cost (new car): Calculate the total gallons of gas used by the new car: $87360$ miles / $40$ miles/gallon.
Calculate repair costs (old car): Total gallons for new car = $87360 / 40 = 2184$ gallons.
Calculate total cost (old car): Calculate the total cost of gas for the new car: $2184 \text{ gallons} * \$2.45/\text{gallon}.$
Calculate total cost (new car): Total gas cost for new car = $2184 \times 2.45 = \$(5350.8)$.
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/\text{year} \times 7 \text{years}$.
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/\text{year} \times 7 \text{years}$. Total insurance for old car = $500 \times 7 = \$(3500)$.
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/year \times 7 $ years.Total insurance for old car = $500 \times 7 = \$3500$.Calculate the total insurance cost for the new car over $7$ years: $\$720/year \times 7 $ years.
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/year \times 7 \text{ years}$. Total insurance for old car = $500 \times 7 = \$3500$. Calculate the total insurance cost for the new car over $7$ years: $\$720/year \times 7 \text{ years}$. Total insurance for new car = $720 \times 7 = \$5040$.
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/year \times 7 \text{ years}$. Total insurance for old car = $500 \times 7 = \$3500$. Calculate the total insurance cost for the new car over $7$ years: $\$720/year \times 7 \text{ years}$. Total insurance for new car = $720 \times 7 = \$5040$. Calculate the total repair costs for the old car over $7$ years: $\$1050/year \times 7 \text{ years}$.
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/year \times 7 $ years.Total insurance for old car = $500 \times 7 = \$3500$.Calculate the total insurance cost for the new car over $7$ years: $\$720/year \times 7 $ years.Total insurance for new car = $720 \times 7 = \$5040$.Calculate the total repair costs for the old car over $7$ years: $\$1050/year \times 7 $ years.Total repairs for old car = $1050 \times 7 = \$7350$.
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/year \times 7 \text{ years}$. Total insurance for old car = $500 \times 7 = \$3500$. Calculate the total insurance cost for the new car over $7$ years: $\$720/year \times 7 \text{ years}$. Total insurance for new car = $720 \times 7 = \$5040$. Calculate the total repair costs for the old car over $7$ years: $\$1050/year \times 7 \text{ years}$. Total repairs for old car = $1050 \times 7 = \$7350$. Assume no repair costs for the new car over $7$ years: $\$0$.
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/year \times 7 $ years.Total insurance for old car = $500 \times 7 = \$3500$.Calculate the total insurance cost for the new car over $7$ years: $\$720/year \times 7 $ years.Total insurance for new car = $720 \times 7 = \$5040$.Calculate the total repair costs for the old car over $7$ years: $\$1050/year \times 7 $ years.Total repairs for old car = $1050 \times 7 = \$7350$.Assume no repair costs for the new car over $7$ years: $\$0$.Calculate the total cost of keeping the old car: $\$8922 $ (gas) + $\$3500 $ (insurance) + $\$7350 $ (repairs).
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/year \times 7 \text{ years}$.Total insurance for old car = $500 \times 7 = \$3500$.Calculate the total insurance cost for the new car over $7$ years: $\$720/year \times 7 \text{ years}$.Total insurance for new car = $720 \times 7 = \$5040$.Calculate the total repair costs for the old car over $7$ years: $\$1050/year \times 7 \text{ years}$.Total repairs for old car = $1050 \times 7 = \$7350$.Assume no repair costs for the new car over $7$ years: $\$0$.Calculate the total cost of keeping the old car: $\$8922 \text{ (gas)} + \$3500 \text{ (insurance)} + \$7350 \text{ (repairs)}$.Total cost for old car = $8922 + 3500 + 7350 = \$19772$.
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/year \times 7 \text{ years}$. Total insurance for old car = $500 \times 7 = \$3500$. Calculate the total insurance cost for the new car over $7$ years: $\$720/year \times 7 \text{ years}$. Total insurance for new car = $720 \times 7 = \$5040$. Calculate the total repair costs for the old car over $7$ years: $\$1050/year \times 7 \text{ years}$. Total repairs for old car = $1050 \times 7 = \$7350$. Assume no repair costs for the new car over $7$ years: $\$0$. Calculate the total cost of keeping the old car: $\$8922 \text{ (gas)} + \$3500 \text{ (insurance)} + \$7350 \text{ (repairs)}$. Total cost for old car = $8922 + 3500 + 7350 = \$19772$. Calculate the total cost of buying the new car: $\$5350.8 \text{ (gas)} + \$5040 \text{ (insurance)} + \$13000 \text{ (purchase price)}$.
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/year \times 7 \text{ years}$. Total insurance for old car = $500 \times 7 = \$3500$. Calculate the total insurance cost for the new car over $7$ years: $\$720/year \times 7 \text{ years}$. Total insurance for new car = $720 \times 7 = \$5040$. Calculate the total repair costs for the old car over $7$ years: $\$1050/year \times 7 \text{ years}$. Total repairs for old car = $1050 \times 7 = \$7350$. Assume no repair costs for the new car over $7$ years: $\$0$. Calculate the total cost of keeping the old car: $\$8922 \text{ (gas)} + \$3500 \text{ (insurance)} + \$7350 \text{ (repairs)}$. Total cost for old car = $8922 + 3500 + 7350 = \$19772$. Calculate the total cost of buying the new car: $\$5350.8 \text{ (gas)} + \$5040 \text{ (insurance)} + \$13000 \text{ (purchase price)}$. Total cost for new car = $500 \times 7 = \$3500$$0$.
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/year \times 7 $ years.Total insurance for old car = $500 \times 7 = \$3500$.Calculate the total insurance cost for the new car over $7$ years: $\$720/year \times 7 $ years.Total insurance for new car = $720 \times 7 = \$5040$.Calculate the total repair costs for the old car over $7$ years: $\$1050/year \times 7 $ years.Total repairs for old car = $1050 \times 7 = \$7350$.Assume no repair costs for the new car over $7$ years: $\$0$.Calculate the total cost of keeping the old car: $\$8922 $ (gas) + $\$3500 $ (insurance) + $\$7350 $ (repairs).Total cost for old car = $500 \times 7 = \$3500$$0$.Calculate the total cost of buying the new car: $500 \times 7 = \$3500$$1$ (gas) + $500 \times 7 = \$3500$$2$ (insurance) + $500 \times 7 = \$3500$$3$ (purchase price).Total cost for new car = $500 \times 7 = \$3500$$4$.Calculate the difference in cost between the new car and the old car: $500 \times 7 = \$3500$$5$ (new car) - $500 \times 7 = \$3500$$6$ (old car).
Calculate cost difference: Calculate the total insurance cost for the old car over $7$ years: $\$500/year \times 7 \text{ years}$. Total insurance for old car = $500 \times 7 = \$3500$. Calculate the total insurance cost for the new car over $7$ years: $\$720/year \times 7 \text{ years}$. Total insurance for new car = $720 \times 7 = \$5040$. Calculate the total repair costs for the old car over $7$ years: $\$1050/year \times 7 \text{ years}$. Total repairs for old car = $1050 \times 7 = \$7350$. Assume no repair costs for the new car over $7$ years: $\$0$. Calculate the total cost of keeping the old car: $\$8922 \text{ (gas)} + \$3500 \text{ (insurance)} + \$7350 \text{ (repairs)}$. Total cost for old car = $8922 + 3500 + 7350 = \$19772$. Calculate the total cost of buying the new car: $\$5350.8 \text{ (gas)} + \$5040 \text{ (insurance)} + \$13000 \text{ (purchase price)}$. Total cost for new car = $500 \times 7 = \$3500$$0$. Calculate the difference in cost between the new car and the old car: $500 \times 7 = \$3500$$1$. Difference in cost = $500 \times 7 = \$3500$$2$.