A mechanic says your radiator has only 40% antifreeze (the rest is water), but it needs to be 80% antifreeze. How much of the solution should be replaced with antifreeze?
(your radiator holds 5 gallons)
The answer is 3 1/3 gallons.
I just don't know how to explain it/do the work on my own???
consider the amount of anti-freeze present. If you replace x gallons with 100%, then the rest (80-x) is still 40%.
.40(5-x) + 1.00x = .80*5
To find out how much of the solution should be replaced with antifreeze, you need to calculate the difference between the desired concentration of antifreeze (80%) and the current concentration (40%). Then, you multiply this difference by the total volume of the solution (5 gallons) to determine the amount of solution that needs to be replaced. Here's how to work it out step by step:
1. Calculate the difference in concentration:
Desired concentration - Current concentration = 80% - 40% = 40%
2. Convert the concentration difference to decimal form:
40% = 40/100 = 0.4
3. Multiply the concentration difference by the total volume of the solution:
0.4 x 5 gallons = 2 gallons
So, you need to replace 2 gallons of the solution with antifreeze to achieve the desired concentration of 80%.