The liquid in a car's radiator is 75% water and 25% antifreeze. Suppose that 30% of the radiator's liquid is drained out and replaced with pure antifreeze. What percent of the radiator's liquid is now antifreeze?
suppose the radiator holds 40 cups (10 qts) ... 30 c water , 10 c antifreeze
12 c drained (.30 * 40) ... 9 c water , 3 c antifreeze
... leaving 21 c water and 7 c antifreeze
refilled with antifreeze
... now has 21 c water and 19 c antifreeze
19 / 40 = ? %
To find the percent of the radiator's liquid that is now antifreeze, we can follow these steps:
Step 1: Calculate the amount of liquid drained out.
Since 30% of the radiator's liquid was drained out, we can represent it as 30% of the initial volume (100%).
So, 30% of the liquid was drained out.
Step 2: Calculate the amount of antifreeze in the remaining liquid.
After 30% of the liquid is drained out, we have 70% of the initial volume remaining.
Since this remaining liquid was initially 25% antifreeze, we have 25% of 70% as antifreeze.
Step 3: Calculate the amount of pure antifreeze added.
Since the drained liquid was replaced with pure antifreeze, the amount of pure antifreeze added is equal to the amount drained out (30% of the initial volume).
Step 4: Calculate the total volume of the new liquid.
To find the total volume, we need to add the amount of remaining liquid to the amount of pure antifreeze added.
Step 5: Calculate the percent of antifreeze in the new liquid.
To find the percent of antifreeze in the new liquid, we divide the amount of antifreeze by the total volume and multiply by 100.
Let's perform the calculations:
Step 1: 30% of the liquid is drained out.
Step 2: 25% of 70% is antifreeze.
(25/100) x 70 = 17.5% of the remaining liquid is antifreeze.
Step 3: 30% of the initial volume is pure antifreeze.
Step 4: 70% + 30% = 100% of the new liquid.
Step 5: (17.5)/(100) x 100 = 17.5% of the new liquid is antifreeze.
Therefore, the percent of the radiator's liquid that is now antifreeze is 17.5%.
To find the percentage of antifreeze in the radiator's liquid after the replacement, we need to understand how the components change during the process.
Let's assume that there is 100 units of liquid in the radiator. Since 75% of the liquid is water and 25% is antifreeze, we have 75 units of water and 25 units of antifreeze.
When 30% of the liquid is drained out and replaced with pure antifreeze, we can calculate the change in the amount of antifreeze and water.
30% of 100 units is (30/100) * 100 = 30 units. This means that 30 units of liquid are drained out.
After draining out 30 units of liquid, we have 100 - 30 = 70 units of liquid remaining in the radiator.
Since 25 units of the remaining liquid are antifreeze, we add the 30 units of pure antifreeze that we added during the process, resulting in a total of 25 + 30 = 55 units of antifreeze.
To calculate the percentage of antifreeze in the remaining liquid, we divide the amount of antifreeze by the total amount of liquid and multiply by 100.
(55 / 70) * 100 = 78.57%
Therefore, after the replacement, approximately 78.57% of the radiator's liquid is antifreeze.