Firefighter Practice Exam

If a truck's radiator currently contains 10 gallons of a 35% antifreeze solution, how much pure antifreeze should be added to achieve a 55% solution?

1. 3.75 gallons

2. 4.44 gallons

3. 5.67 gallons

4. 6.15 gallons

The correct answer is: 4.44 gallons

To determine how much pure antifreeze should be added to the existing 35% antifreeze solution to achieve a final concentration of 55%, we can set up the equation based on the given information. Initially, the truck's radiator contains 10 gallons of a 35% antifreeze solution. This means there are 3.5 gallons of pure antifreeze in it (0.35 * 10 = 3.5). When we add pure antifreeze, let’s denote the amount of pure antifreeze to be added as \( x \). After adding \( x \) gallons of pure antifreeze, the total amount of solution becomes \( 10 + x \) gallons, and the total amount of pure antifreeze becomes \( 3.5 + x \) gallons. To reach a 55% antifreeze solution, we need to set up the following equation: \[ \frac{3.5 + x}{10 + x} = 0.55 \] Now we multiply both sides of the equation by \( 10 + x \) to eliminate the fraction: \[ 3.5 + x = 0.55(10 + x) \] Expanding the right side gives us: \[