Question

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar, and the second brand contains 15% vinegar. The chefwants to make 200 milliliters of a dressing that is 13% vinegar. How much of each brand should she use?

Answer 1

F is the number of ml of the first brand

S is the number of ml of the second brand

The first equation is

$F+S=200$

and for the second equation

$0.05F+0.15S=.13(200)$

we will let by itself F of the first equation

$F=200-S$

We will substitute the value of F in the second equation

$0.05(200-S)+0.15S=.13(200)$

then we simplify the expression

$10-0.05S+0.15S=26$$10+0.1S=26$

then we let by itself S

$S=\frac{26-10}{0.1}=160$

then we substitute the value of S in the equation with F isolate

$F=200-160=40$

Therefore

The chef will need 40 ml of the first brand and 160 ml of the second brand