# A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 12% vinegar. The chef wants to make 200 mL of a dressing that is 11% vinegar. How much of each brand should she use?

##### 2 Answers

brand 1 =40ml

brand 2=160ml

#### Explanation:

Let the amount of brand 1 be

Let the amount of brand 2 be

The target is to have 1 equation with just 1 unknown, thus solvable.

Using

Multiply both sides by 100

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Using Equation (1) substitute for

Multiply both sides by (-1)

Divide both sides by 5

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A different approach - we can represent this using a graph

The actual explanation is a bit long. However, once you understand the principle the calculation is very fast. May be 4 or 5 lines.

#### Explanation:

**The final blend will always be 200 ml no matter what the proportion of each of the two constituents.**

Let the first dressing containing 7% vinegar be

Let the second dressing containing 12% vinegar be

Let the unknown volume of the 12% dressing be

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Suppose the 200ml contained only

Suppose the 200ml contained only

As you blend them in different ratios then the final vinegar content of that blend would be directly related to how much of each type you use. This final vinegar content will be somewhere between the two extremes of 7% and 12%

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If you know how much of say the 7% dressing there is then the amount of the 12% dressing is: 200ml - the volume of the 7% dressing.

So by considering just one of them there is an indirect link to the other. Thus by considering the change in the amount of one of them and observing the change in blended vinegar content we are indirectly observing everything

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Multiply both sides by

But