Solving a percent mixture problem

Question

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 6% vinegar, and the second brand contains 11% vinegar. The chef wants to make 350 millileters of a dressing that is 7% vinegar. How much of each brand should she use? 

Answer 1

Let x represent mL of 6% solution and y represent mL of 11% soltion

 

I will list the steps first.  If you get stuck scroll on down to see the solution.

 

1) Write an equation that relates x, y and 350

 

2) The amount of vinegar in solution 1 + the amount of vinegar in solution 2 = the amount of vinegar in the final solution.  To find the amount of vinegar in a solution multiply the percentage time the number of mL of that solution.

 

Write an equation that relates 0.06, x, 0.11, y, 0.07 and 350

 

3) Solve the two equations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Solution.

 

eq1)  x+y=350

eq2)  0.06x+0.11y=0.07(350)      simplifying 0.06x+0.11y=24.5  multiply each term by 100 gives 6x+11y=2450

 

Solve the first equation for either x or y and substitute into the second equation.

 

x=350-y

6(350-y)+11y=2450

2100-6y+11y=2450

5y=350

y=350/5=70

x=350-70=280

 

Use 70mL of the 11% solution and 280mL of the 6% solution