Respuesta :
Answer:
She should mix 20 ounces of 16% solution and 12 ounces of 8% solution.
Step-by-step explanation:
Given:
Doreen Schmidt needs to prepare 32 ounces of a 13% hydrochloric acid solution.
Now, to find the amount she should mix of 16% solution and of 8% solution.
Let the 16% solution amount be [tex]x.[/tex]
And let the 8% solution amount be [tex]y.[/tex]
So, the total ounces of solution:
[tex]x+y=32[/tex]
[tex]y=32-x[/tex] .......(1)
Now, to solve the equation to get the solution she should mix:
[tex]16\%\ of\ (x)+8\%\ of\ (y)=13\%\ of\ (32)\\\\\frac{16}{100}\times x+\frac{8}{100}\times y=\frac{13}{100}\times 32[/tex]
[tex]0.16x+0.08y=0.13\times 32[/tex]
Substituting the value of [tex]y[/tex] from equation (1) we get:
[tex]0.16x+0.08(32-x)=4.16[/tex]
[tex]0.16x+2.56-0.08x=4.16[/tex]
[tex]2.56+0.08x=4.16[/tex]
Subtracting both sides by 2.56 we get:
[tex]0.08x=1.6[/tex]
Dividing both sides by 0.08 we get:
[tex]x=20.[/tex]
The 16% solution amount = 20 ounces.
Now, substituting the value of [tex]x[/tex] in equation (1) we get:
[tex]y=32-x\\\\y=32-20\\\\y=12.[/tex]
The 8% solution amount = 12 ounces.
Therefore, she should mix 20 ounces of 16% solution and 12 ounces of 8% solution.
