a chef is using amixture of two brands of italian dressing. the frist brand contains 6% vinger, the chef wants to make 310

Question

a chef is using a mixture of two brands of Italian dressing. the first brand contains 6% vinger, the second brand contains 11% vinger. the chef wants to make 310 milliters of dressing that is 8% vinger. how much of brand should she use.

 

 

first brand=

second brand=

 

Answer 1

You want to setup an equation that will match the word problem. Let's call the amount of the first brand, F and the amount of the second brand, S.

 

We want the total mixture to be 310mL so: F + S = 310

 

Also, you want the total mixture to contain 8% vinegar so: .06F + .11S = .08(310)

 

Now, we can solve the system of equations using substitution.

 

F + S = 310

.06F + .11S = .08(310)

 

F = 310 - S      [solve 1st equation for F]

.06(310 - S) + .11S = .08(310)     [substitute into 2nd equation]

18.6 -.06S +.11S = 24.8

.05S = 6.2

S = 124

 

F + 124 = 310     [substitute answer for S back into original equation]

F = 186

 

Answer: to make a 310mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.