Final answer:
The equation to calculate the quantities is 0.15x + 0.60(60 - x) = 0.45 × 60, with x representing the gallons of 15% antifreeze solution. Solving the equation determines that 20 gallons of the 15% solution and 40 gallons of the 60% solution are required to achieve the desired mixture.
Step-by-step explanation:
To determine how many gallons of a 15% antifreeze solution should be mixed with a 60% antifreeze solution to produce 60 gallons of a 45% antifreeze solution, we can use the concept of mixtures in algebra. We set up an equation where the total amount of pure antifreeze from both solutions equals the amount of pure antifreeze in the final mixture.
Let x be the gallons of 15% solution needed, so 60 - x will be the gallons of 60% solution. The equation modeling this situation is:
0.15x + 0.60(60 - x) = 0.45 × 60
Solving for x gives:
0.15x + 36 - 0.60x = 27
-0.45x = -9
x = 20
So, 20 gallons of 15% antifreeze solution and 40 gallons (since 60 - 20 = 40) of 60% antifreeze solution are needed.