## 28. Fuel Tanks Full of Gasoline

Someone has two cars, a larger one and a small one. Their fuel tanks have a combined capacity of 70 liters. When both tanks are empty, the car owner must pay 45 francs to fill one tank and 68 francs to fill the other. Suppose this person uses regular gasoline for the small car and premium gasoline for the larger car, and the difference in cost per liter between regular gasoline and premium gasoline is 29 cents (cent - one hundredth of a franc).

What is the capacity of the fuel tanks of each of the two cars?
28. Let $x$ be the capacity of the tank of a small car, and $X$ of a large car; let $p$ denote the price in francs of one liter of regular gasoline. We have the following system of equations:

$$
\begin{gathered}
x+X=70 \\
x p=45 \\
X(p+0.2)=68
\end{gathered}
$$

Multiplying the last equation by $x$ and eliminating $p$ from the result, we get

$$
x+X=70 \text { and } 45 X+0.2 x X=68 x .
$$

Now, eliminating $X$ from this system, we get

$$
2 x^{2}+990 x-31500=0
$$

or

$$
(x-30)(2 x+1050)=0
$$

216

The only acceptable solution is $x=30$ liters and, therefore, $X=40$ liters.

Thus, the tank of the small car holds 30 liters of gasoline, and the tank of the large car holds 40 liters.