help please word problem

Question

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 8%

 vinegar, and the second brand contains 13%

 vinegar. The chef wants to make 310

 milliliters of a dressing that is 9%

 vinegar. How much of each brand should she use?

Firstbrand:

milliliters

Answer 1

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 8% vinegar, and the second brand contains 13% vinegar. The chef wants to make 310 milliliters of a dressing that is 9% vinegar. How much of each brand should she use?

Given:

Brand A = 8% Vinegar

Brand B = 13% Vinegar

Chef wants 310mL 9% Vinegar

Find:

How much of each brand should he use?

________________________________________________________________________

Define variables

Let Va= amount of 8% Vinegar (in mL)

Let Vb= amount of 13% Vinegar (in mL)

________________________________________________________________________

Write Equations

The amount of Va and the amount of Vb added together should equal the total amount the chef wants

Va + Vb = 320 mL

The salad dressing final concentration should be 9%. So we can add the amount of each vinegar times their concentration to get to the total amount at the right concentration.

(0.08)Va + (0.13)Vb = (0.09)(310mL)

____________________________________________________________________________

Solve your system of equations (I will use substitution)

Va + Vb = 310 mL

Va = 320 - Vb

(0.08)Va + (0.13)Vb = (0.09)(310mL)

(0.08)(320-Vb) + (0.13)Vb = (0.09)(310mL)

25.6 - 0.08Vb + 0.13Vb = 27.9

0.05Vb = 3.1

Vb = 62mL

Va = 310-Vb = 248mL

So you will need 248mL of the 8% and 62mL of the 13% to get 310mL of the 9%

Hope this Helps!!