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A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 12%
vinegar. The chef wants to make 160 milliliters of a mixture that contains 23% vinegar. How much vinegar and how much Italian dressing should she use?

Respuesta :

luisejr77

Answer:

Amount of  vinegar. 100% : 20 milliliters

Amount of  Italian dressing: 140 milliliters

Step-by-step explanation:

Let's call A the amount of  vinegar. 100%

Let's call B the amount of  Italian dressing . 12% vinegar

The resulting mixture should have 23%  vinegar, and 160 milliliters.

Then we know that the total amount of mixture will be:

[tex]A + B = 160[/tex]

Then the total amount of pure antifreeze in the mixture will be:

[tex]A + 0.12B = 0.23 * 160[/tex]

[tex]A + 0.12B = 36.8[/tex]

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -1 and add it to the second equation:

[tex]-A -B = -160[/tex]

[tex]-A -B = -160[/tex]

               +

[tex]A + 0.12B = 36.8[/tex]

--------------------------------------

[tex]-0.88B = -123.2[/tex]

[tex]B = \frac{-123.2}{-0.88}[/tex]

[tex]B = 140\ milliliters[/tex]

We substitute the value of B into one of the two equations and solve for A.

[tex]A + 140 = 160[/tex]

[tex]A = 20\ milliliters[/tex]

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