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

 

 

Brand 1 is 5% vinegar or .05 * Total of Brand 1

 

Brand 2 is 15% vinegar or .15 * Total of Brand 2

 

 

Chef wants to make 390 milliliters that is 8% vinegar = 390 ml that is .08 (390) so we can multiply and see that we have 31.2 ml that is vinegar.

 

Let x = Total amount of Brand 1

 

y =  Total amount of Brand 2

 

Brand 1 + Brand 2 = 390 ml, so x + y = 390 ml

 

subtract y, so x = 390 - y

 

.05x is amount of Vinegar in Brand 1

.15y is amount of Vinegar in Brand 2

 

So .05x + .15y = 31.2ml

 

We have 2 equations in two unknowns. I am going to do some substitution to get 1 equation in 1 unknown.

 

.05( 390-y) + .15y = 31.2  Distribute next

19.5ml -.05y + .15y = 31.2 ml

 

Combining:  19.5ml + .10y= 31.2 ml

Subtract:   .10y = 11.7 ml

Divide by .10 and y = 117 ml

 

So since y is the amount we need of Brand 2, then using what we know

 

x= 390 - 117

 

x = 273 ml of Brand 1

 

Checking: x + y should equal 390

 273 + 117 = 390

 

and .05(273) + .15(117) = .08( 390)

 

13.65 + 17.55 = 31.2

 

31.2 = 31.2

 

Voila!