Math Problem I need help with

Question

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar, and the second brand contains 13% vinegar. The chef wants to make 320 milliliters of a dressing that is 12% vinegar. How much of each brand should she use?

First Brand= _ mL

Second Brand= _ mL

Answer 1

320(.12) = x(.13)+ (320-x)(.05) solve for x = amount of 13%, then find 320-x = amount of 5%

.13x -.05x = 320(.12-.05) = 320(.07)= 22.4

22.4 = .13x -.05x

.08x = 22.4

x = 2240/8 = 280 ml of 13%

320-280 = 40 ml of 5%

13-12 = 1

12-5 = 7 should be 7 times as much 13% as 5%

280 = 7 times 40. BINGO

Answer 2

Let's choose 2 variables:

1. x = 5% vinegar brand
2. y = 13% vinegar brand

We know that the total volume of the dressing is 320 mL. So, the total mixture of x and y will end up being a volume of 320 mL as shown below. We will call this Equation1:

x + y = 320

We also know that we want the total concentration to be 12% of the 320 mL after both vinegar concentrations are added. This gives us Equation2:

0.05x + 0.13y = 0.12(320)

0.05x + 0.13y = 38.4

We will rearrange Equation1 so we can substitute x and solve for y in Equation2:

x = 320 - y

Now, we substitute and solve:

0.05(320-y) + 0.13y = 38.4

16 - 0.05y + 0.13y = 38.4

16 + 0.08y = 38.4

0.08y = 12.4

y = 155 mL

Finally, we solve for x by plugging the y value into the rearranged Equation1:

x = 320 - y

x = 320 - (155)

x = 165 mL