how many liters of a 60% antifreeze solution should be added to 9 liters of a 30% solution to get a 50% antifreeze solution
18 liters
To find out how many liters of a 60% antifreeze solution should be added to 9 liters of a 30% solution to obtain a 50% antifreeze solution, use the following steps:
Step 1: Let x be the number of liters of the 60% antifreeze solution needed.
Step 2: Calculate the amount of antifreeze in the 30% solution:
30% of 9 liters = 0.30 * 9 = 2.7 liters of antifreeze
Step 3: Calculate the amount of antifreeze in the 60% solution:
60% of x liters = 0.60 * x = 0.6x liters of antifreeze
Step 4: Calculate the amount of antifreeze in the resulting 50% solution:
50% of (9 + x) liters = 0.50 * (9 + x) = 4.5 + 0.5x liters of antifreeze
Step 5: Set up an equation:
The amount of antifreeze in the 30% solution + the amount of antifreeze in the 60% solution = the amount of antifreeze in the resulting 50% solution
2.7 + 0.6x = 4.5 + 0.5x
Step 6: Simplify the equation by combining like terms:
0.6x - 0.5x = 4.5 - 2.7
0.1x = 1.8
Step 7: Solve for x by dividing both sides of the equation by 0.1:
x = 1.8 / 0.1
Step 8: Calculate the value of x:
x = 18
Therefore, 18 liters of a 60% antifreeze solution should be added to 9 liters of a 30% solution to obtain a 50% antifreeze solution.
To solve this problem, we need to use a formula called the "mixture" or "weighted average" formula. The formula is:
(Amount of Solution 1) x (Concentration of Solution 1) + (Amount of Solution 2) x (Concentration of Solution 2) = (Amount of Mixture) x (Concentration of Mixture)
Let's plug in the values given in the question:
9 liters x 30% + (Amount of 60% solution) x 60% = (9 liters + Amount of 60% solution) x 50%
Now, let's solve for the amount of 60% antifreeze solution:
9(0.3) + (Amount of 60% solution)(0.6) = (9 + Amount of 60% solution)(0.5)
2.7 + (Amount of 60% solution)(0.6) = 4.5 + 0.5(Amount of 60% solution)
0.6(Amount of 60% solution) - 0.5(Amount of 60% solution) = 4.5 - 2.7
0.1(Amount of 60% solution) = 1.8
(Amount of 60% solution) = 1.8 / 0.1
(Amount of 60% solution) = 18
Therefore, you would need to add 18 liters of the 60% antifreeze solution to get a 50% antifreeze solution.
L*.6+9*.3=(L+9).5
solve for L