I need someone to solve my word problem

Question

A chef is using a mixture of two brands of Italian dressing. The first brand contains
5%
vinegar, and the second brand contains
15%
vinegar. The chef wants to make
360
milliliters of a dressing that is
6%
vinegar. How much of each brand should she use?

Answer 1

360 ml of 6% vinegar means that salad dressing contains 0.06(360) = 21.6 ml of vinegar.

 

 

Let x be the ml of the first brand (5% vinegar) that she will use.

That amounts to 0.05x ml of vinegar used in the first brand.

 

If she is going to use a total of 360 ml of salad dressing,

then she must use 360 - x ml of the second brand (15% vinegar).

That means it will contain 0.15(360 - x) ml of vinegar.

 

The amounts of vinegar should add up.

 

0.05x + 0.15(360 - x) = 21.6 (multiply both sides by 100 to get rid of the fractions)

 

5x + 15(360 - x) = 2160

 

5x + 5400 - 15x = 2160

-10x = -3240

x = 324

360 - x = 36

 

How much of each brand should she use?

 

She should use

   324 ml of the fist brand and

    36 ml of the second brand

   

Answer 2

She should use 324 ml of the first brand and 36 ml of the second brand.

 

The equation is:  (360) (.06) = (x) (.05) + (360-x) (.15), where "x" is the number of milliliters to be used from the first brand and (360-x) is the amount to be used from the second brand.

 

Multiplying out, we get 21.6 = .05x  + 54.0 - .15x

 

Subtract 54 from each side:   21.6 -54.0 = .05x - .15x

 

Calculate:   - 32.4 = -.10x

 

Multiply both sides by -10:  324 = x.  

 

The first brand is 324 ml of the mix.  The second brand is 360 ml -324 ml, or 36 ml, of the mix.