Help with this word problem please

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 390 milliliters of a dressing that is 8% vinegar. How much of each brand should she use?

 

I need to solve for brand 1 and brand 2.

Answer 1

This question is solved by using the formula C1V1 + C2V2 = C3V3, where C = concentration and V = volume

 

in essence, the 5% vinegar will be used to dilute the 15% vinegar

 

to make the calculations easier, we will convert the % figures to decimals,

so 5% = 0.05, 8% = 0.08, and 15% = 0.15

let x = the volume of 15% vinegar

then 0.15x + 0.05(390 - x) = 0.08(390)

our equation becomes 0.15x + 19.5ml - 0.05x = 31.2ml

combining, we get 0.1x = 11.7ml

solving, x = 117ml

 

so, we need 117ml of 15% vinegar to which we will add 273ml of 5% vinegar to make 390ml of 8% vinegar

 

Proof: 117ml x 0.15 + 273ml x 0.05 = 390 x 0.08

17.55ml of pure vinegar + 13.65ml of pure vinegar = 31.2ml of pure vinegar; 31.2ml = 31.2ml