Question

A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 12% vinegar. The chef wants to make 320 milliliters of a mixture that contains 23% vinegar. How much vinegar and how much Italian dressing should she use?Vinegar:Italian dressing:Solve by percent mixture using system of linear equations.

Answer 1

Answer:

• Vinegar: 40 milliliters

• Italian dressing: 280 milliliters

Explanation:

Let the amount of vinegar to be used = x

Let the amount of Italian dressing to be used = y

The chef wants to make 320 milliliters of the mixture.

$x+y=320\cdots(1)$

The chef plans to mix 100% vinegar with Italian dressing(12% vinegar) to make 320 milliliters of a mixture that contains 23% vinegar.

$\begin{gathered} (100\%\text{ of x\rparen+\lparen12\% of y\rparen=23\% of 320} \\ \implies x+0.12y=73.6\cdots(2) \end{gathered}$

Thus, we have a system of linear equations.

$\begin{gathered} x+y=320\operatorname{\cdots}(1) \\ x+0.12y=73.6\operatorname{\cdots}(2) \end{gathered}$

Subtract (2) from (1):

$0.88y=246.4$

Divide both sides by 0.88

$\begin{gathered} \frac{0.88y}{0.88}=\frac{246.4}{0.88} \\ y=280 \end{gathered}$

Using equation (1), we solve for x:

$\begin{gathered} x+y=320 \\ x+280=320 \\ x=320-280 \\ x=40 \end{gathered}$

Therefore, the chef should use 40 milliliters of Vinegar and 280 milliliters of Italian dressing.