Question 104
1. Car Flex - A car is called Flex if it can be fueled with gasoline or alcohol. Assume that the prices of alcohol and gasoline are, respectively, $\mathrm{R}\$ 1,59$ and $\mathrm{R}\$ 2,49$ per liter.
a. Suppose a flex car runs $12,3~\mathrm{km}$ per liter of gasoline, which we indicate $12,3~\mathrm{km}/\mathrm{l}$. What should be the ratio $\mathrm{km}/\mathrm{l}$ of this car, for alcohol, so that the use of alcohol is financially more advantageous than that of gasoline?
b. If the performance of a flex car is $x~\mathrm{km}/\mathrm{l}$ with gasoline and $\left(\frac{x}{2}+1\right)~\mathrm{km}/\mathrm{l}$ with alcohol, write the expression of the function $g(x)$ that provides the cost of this car rotating $100~\mathrm{km}$ using gasoline and the expression of the function $a(x)$ that provides the cost of this car run $100~\mathrm{km}$ using alcohol.
c. For the cost to be the same, both with alcohol and gasoline, what should be the ratio $\mathrm{km}/\mathrm{l}$ for gasoline and alcohol?
d. In what condition is the use of alcohol more financially advantageous than that of gasoline? Give a numerical example that satisfies the condition.
a. Suppose a flex car runs $12,3~\mathrm{km}$ per liter of gasoline, which we indicate $12,3~\mathrm{km}/\mathrm{l}$. What should be the ratio $\mathrm{km}/\mathrm{l}$ of this car, for alcohol, so that the use of alcohol is financially more advantageous than that of gasoline?
b. If the performance of a flex car is $x~\mathrm{km}/\mathrm{l}$ with gasoline and $\left(\frac{x}{2}+1\right)~\mathrm{km}/\mathrm{l}$ with alcohol, write the expression of the function $g(x)$ that provides the cost of this car rotating $100~\mathrm{km}$ using gasoline and the expression of the function $a(x)$ that provides the cost of this car run $100~\mathrm{km}$ using alcohol.
c. For the cost to be the same, both with alcohol and gasoline, what should be the ratio $\mathrm{km}/\mathrm{l}$ for gasoline and alcohol?
d. In what condition is the use of alcohol more financially advantageous than that of gasoline? Give a numerical example that satisfies the condition.