Question

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?

Answer 1

Amount of vinegar. 100% : 20 milliliters

Amount of Italian dressing: 140 milliliters

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:

`A + B = 160`

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

`A + 0.12B = 0.23 * 160`

`A + 0.12B = 36.8`

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:

`-A -B = -160`

`-A -B = -160`

+

`A + 0.12B = 36.8`

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

`-0.88B = -123.2`

`B = (-123.2)/(-0.88)`

`B = 140\ milliliters`

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

`A + 140 = 160`

`A = 20\ milliliters`