to conduct a scientific experiment, students need to mix 90 millimeters of a 3% acid solution. They have a 1% solution and a 10% solution available. How many millimeters of a 1% solution and of the 10% solution should be coming to produce 90 millimeters of the 3% solution
.01x + .01y=90?
.01x + .03y=90?
To solve this problem, let's assume that x represents the millimeters of the 1% solution and y represents the millimeters of the 10% solution.
We are given that the total volume of the mixture is 90 millimeters and that the acid concentration in the final solution should be 3%.
The acid concentration in the 1% solution is 0.01 (1% is equivalent to 0.01). Therefore, the amount of acid in the 1% solution is 0.01x.
Similarly, the acid concentration in the 10% solution is 0.1 (10% is equivalent to 0.1). Therefore, the amount of acid in the 10% solution is 0.1y.
In the final mixture, the total amount of acid is the sum of the acid amounts from the two solutions. So we have the equation:
0.01x + 0.1y = 0.03 * 90
Simplifying the equation:
0.01x + 0.1y = 2.7
To solve this equation, we have multiple ways available. One common approach is to use the method of substitution or elimination. Let's solve it using substitution:
1) Rearrange the equation:
0.01x = 2.7 - 0.1y
2) Solve for x:
x = (2.7 - 0.1y) / 0.01
Now, we substitute this value of x in either of the original equations mentioned in your question:
0.01((2.7 - 0.1y) / 0.01) + 0.1y = 2.7
Simplifying the equation:
2.7 - 0.1y + 0.1y = 2.7
We see that the 0.1y term cancels out, leaving us with:
2.7 = 2.7
This equation is an identity, meaning that it holds true for all values of y. Therefore, the system of equations is consistent, and we have infinitely many solutions.
In this case, it means there are multiple combinations of the 1% and 10% solutions that can be mixed to obtain 90 millimeters of the 3% solution. The values of x and y can be any pair of numbers that satisfy the equation.