Question

A scientist has two solution, which she is labeled. solution A and solution B. each contains salt. she knows that solution A is 35% salt and solution B is 60% salt. she want to obtain 50 ounces of a mixture that is 45% salt. how many ounces of each solution should she use

Answer 1

Step 1. Define our variables.

"x" will represent the ounces of the solution A

"y" will represent the ounces of the solution B.

Step 2. Define and equation for the total ounces of the solution mix.

Since we have to add the quantities x and y to get the solution, and we are told that the total of ounces is 50.

The sum of the ounces of solution A "x" and the sum of the ounces of solution B "y" must be equal to 50 ounces:

`x+y=50`

Step 3. Define a second equation for the percentage of salt.

solution A has 35% salt. Thus, in A, which has "x" ounces, we will have that 35% of x is salt:

`0.35x`

Note: we represent 35% as 0.35

Solution B has 60% of salt. Thus, in B, which has "y" ounces, we will have that 60% of y is salt:

`0.6y`

Note: we represent 60% as 0.6

Since the final mix (which has 50 ounces) has 45% of salt, the amount of salt is:

`0.45(50)=22.5`

Note: we represent 45% as 0.45

We add the amount of salt in A 0.35x, and the amount of salt in B 0.6y to get the amount of salt in the mix:

`0.35x+0.6y=22.5`

Step 4. Solve the system of equations.

The system of equation is:

`\begin{gathered} 0.35x+0.6y=22.5 \\ x+y=50 \end{gathered}`

To solve this, we need to eliminate one variable.

Step 5. Multiply the second equation by (-0.35), the system now is:

`\begin{gathered} 0.35x+0.6y=22.5 \\ -0.35x-0.35y=-17.5 \end{gathered}`

Note: the -17.5 is the result of -0.35x50

Step 6. Add the two equations to eliminate x:

Step 7. From the resulting equation of the last step, solve the equation for y:

`\begin{gathered} 0.25y=5 \\ y=(5)/(0.25) \\ y=20 \end{gathered}`

Step 8. Substitute this value of y into one of the original equations of the system, to find x.

We substitute y in the equation:

`x+y=50`

since y=20:

`x+20=50`

solving for x:

`\begin{gathered} x=50-20 \\ x=30 \end{gathered}`

Answer:

how many ounces of each solution should she use​?

since x=30, she should use 30 ounces of solution A.

And since y=20, she sould use 20 ounces of solution B.