algebra answers please

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 370

milliliters of a dressing that is 7%

vinegar. How much of each brand should she use?

Firstbrand:

milliliters

Secondbrand:

milliliters

Answer 1

A substitution should work here. You want to blend two salad dressings to make 370 mls of a new combination at 7% vinegar.

Let the salad dressing with 11% vinegar be x

Let the salad dressing with 6% vinegar be y

x + y = 370

So y = 370 - x

And

0.11x + .06y = .07(370)

We can substitute 370 - x for y

0.11x + .06(370 - x) = 25.9

0.11x + 22.2 - .06x = 25.9

Next we subtract 22.2 from both sides of the equation and combine like terms

0.11x -.06x = 25.9 - 22.2

0.05x = 3.7

Divide both sides of the equation by .05

x = 74

So we need 74 mls of x at 11%

We can substitute 74 for x in the original equation x + y = 370 to find y

y = 370 - x

y = 370 - 74 = 296 we need 296 mls at 6%

We need 74 mls at 11% and 296 mls at 6% to make 370 mls at 7%

Checking

0.11(74) - .06(370 -74) = .07(370)

8.14 + 17.76 = 25.9

25.9 = 25.9

I hope you find this useful if you have any questions please leave me a message.