Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 140 ounces of a mixture that is 80% salt. How many ounces of each solution should she use?

Answer 1

Let x be the number of ounces of Solution A that the scientist uses, and let y be the number of ounces of Solution B that she uses. We can set up the following system of equations to represent the given information:

0.65x + 0.90y = 140 * 0.80 = 112
x + y = 140

To solve this system of equations, we can first multiply the second equation by -1 and add the resulting equations:

-1 * (x + y = 140)
-x - y = -140

0.65x + 0.90y = 112
-x - y = -140

-0.35x - 0.10y = -28

Next, we can divide both sides of the second equation by -0.1 to get rid of the fractional coefficient:

-0.35x - 0.10y = -28
(-0.1/-0.1) * (-0.35x - 0.10y) = (-0.1/-0.1) * -28
-3.5x - y = -28

Finally, we can add the resulting equations to eliminate one of the variables:

-3.5x - y = -28
0.65x + 0.90y = 112

0.35x + 0.90y = 84

Dividing both sides by 0.35, we find that x = 240.

Substituting this value back into the equation x + y = 140, we find that y = -100. Since y represents the number of ounces of Solution B, this is not a valid solution. This means that there is no solution to the system of equations, and the scientist cannot obtain a mixture that is exactly 80% salt using these two solutions.