Question

During a general maintenance check, a mechanic notices that the radiator antifreeze solution in a particular truck has dropped below a recommended safe level. If the radiator to this truck currently contains 10 gallons of a 35% antifreeze solution, what quantity of pure antifreeze must be added to acquire a 55% antifreeze solution? (Note: Assume the truck's radiator capacity can accommodate the additional antifreeze without draining any of the existing solution.)

A. 3.75 gallons

B. 4.44 gallons

C. 5.67 gallons

D. 6.15 gallons

Answer 1

To acquire a 55% antifreeze solution, approximately 4.44 gallons of pure antifreeze must be added to the current solution of 10 gallons of a 35% antifreeze solution.

Step-by-step explanation:

To find the quantity of pure antifreeze that must be added to acquire a 55% antifreeze solution, you can set up an equation using the concept of mixtures.

Let x represent the quantity of pure antifreeze that needs to be added.

The total amount of antifreeze in the final solution will be the current amount of antifreeze (10 gallons) plus the quantity of pure antifreeze added (x gallons).

The equation is then:

10 gallons * 35% antifreeze + x gallons *100% antifreeze = (10 gallons + x gallons) * 55% antifreeze

Simplifying this equation, we get:

3.5 + 1x = 5.5 + 0.55x

0.45x = 2

x = 2 / 0.45

x ≈ 4.44 gallons

Therefore, approximately 4.44 gallons of pure antifreeze must be added to acquire a 55% antifreeze solution.