MaryLane B. answered • 04/29/15

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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!