Need a little help with an Algebra 2 problem

Question

A chef is using a mixture of two brands of Italian dressing. The first brand contains 9% vinegar, and the second brand contains 14% vinegar. The chef wants to make 210 milliliters of a dressing that is 11% vinegar. How much of each brand should she use?

Answer 1

First, it is important to realize that to solve this problem, we will need to get two sets of information: the amounts of vinegar that we are adding together, and the amounts of dressing we are adding together.

 

Let x be the amount of the first dressing we use (with 9% vinegar) AND

let y be the amount of the second dressing (with 14% vinegar).

 

This means that 0.09x is the amount of vinegar we get whenever we use x amount of the first dressing, AND

0.14y is the amount of vinegar we get whenever we use y amount of the second dressing.

 

Here are the two equations that are needed:

 

x + y = 210 mL (combine the dressings together to get the volume of the final dressing)

0.09x + 0.14y = 0.11(210) ... (combine the amounts of vinegar to get the volume of vinegar in the final dressing)

 

Solve for x and y.

 

Good luck!

 

Answer 2

Let x = number of ml of 9% vinegar dressing

     210 - x = number of ml of 14% vinegar dressing

     210 = number of ml of 11% vinegar dressing

 

To find the amount of vinegar in a given type of dressing, multiply the number of ml of dressing by the percentage of vinegar in the dressing.

 

So, 0.09x + 0.14(210-x) = 0.11(210)

 

      0.09x + 29.4 - 0.14x = 23.1

 

                             -0.05x = -6.3

 

                                      x = 126 ml

 

Use 126 ml of 9% vinegar dressing with 84 ml of 14% vinegar dressing to obtain 210 ml of 11% vinegar dressing.  

Answer 3

 let us assume he takes x ml of first brand and y ml of second brand

amount of vinegar  is  9x/100 + 14y/100

 

x+y = 210 and  9x/100+ 14y / 100 =( 11/100)210

 

solve these 2 equations to get the value of x and y