A chef is going to use a mixture of two brands of Italian dressing.

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
200
milliliters of a dressing that is
11%
vinegar. How much of each brand should she use?

Answer 1

Mahdi,

 

this is a two equations in two unknowns question.

assume q1 = quantity of dressing 1

and q2= quantity of dressing 2

 

equation 1 - the problem states that the final quantity is 200 ML

then q1 + q2 = 200

 

equation 2 - the vinegar concentration in the final mix is equal to the combined vinegar concentration from the 2 dressings, then

11% X 200 = 8% X q1 + 13% x q2

22 = 0.08q1 + 0.13q2

 

from equation 1, q1 = 200 - q2

substitute in equation 2, then

22 = 0.08 (200 - q2) + 0.13q2

22 = 16 - 0.08q2 + 0.13q2

0.05q2 = 6

then q2 = 120 ML and q1 = (200 - 120) = 80 ML

 

the chef needs to use 80 ML from dressing 1 and 120 ML from dressing 2

 

good luck

 

 

Answer 2

let x = number of milliliters of 8% (0.08) vinegar

 

let y = number of milliliters of 13% (0.13) vinegar

 

then:  x + y = 200  -------------------------------------------------->  13x + 13y = 13(200) ---> 13x + 13y = 2600

 

also:  0.08x + 0.13y = 0.11(200) ---> 8x + 13y = 11(200) --->                                           8x + 13y = 2200

 

subtracting the bottom equation from the top equation ---> 5x = 400 ---> x = 80,

 

then, from x + y = 200 ---> y = 200 - x = 200 - 80 ----------------------> y = 120