Question

A chef is using a mixture of two brands of Italian dressing. The first brand contains 9% vinegar and the second brand contains 14% vinegar. The chef wants to make 400 milliliters of a dressing that is 11% vinegar. How much of each brand should she use?

Answer 1

You can put this solution on YOUR website!
I am a visual learner, so I try to draw a picture to help me understand a word problem. In a mixture problem, you are working with an amount(ml) and a concentration(%).
I draw 3 lines ___+___=___ (I usually use boxes instead of lines to combine the #'s and variables)
Let your first brand = x
Let your second brand = y
You do not need a variable for the product because you have an amount and a concentration already. Use the variables (x and y) to replace your unknowns. The unknowns are the amounts of the first and second brands.
x+y=320 (this is your equation for the amounts)
0.08x +0.13y=.11(320) (this is your equation for the concentrations)
We can use the substitution or elimination method to solve this. I will use the substitution method. I don't like using decimals, so I am going to move the decimal place two units to the right to make them whole numbers. This gives me: 8x+13y=11(320)


Using substitution on the first equation, I put X on one side of the equation. This gives me x=(-y+320). I can now substitute (-y+320) for x in the second equation.
8(-y+320)+13y=3520
-8y+2560+13y=3520
Subtract 2560 from both sides and combine 13y and -8y. This gives you 5y=960. Divide both sides of the equation by 5. This gives you y=192.
y=192
x=128
I got x by plugging y into equation #1.
x+(192)=320. After subtracting 192 from 320, I get x= 128.
To check your answer, always substitute x and y in for both equations.
ANSWER: The chef should use 128 milliliters of the 8% vinegar brand and 192 milliliters of the 13% vinegar brand.

Answer 2

thank you both

Answer 3

Can I have a medal or a fan or both please

Answer 4

wait, how did get 8 and 13. The amounts are 9 and 14? I'm confused

Answer 5

Um give me a minute to think

Answer 6

one step ahead of you @Jannah☺️ I already fanned you both

Answer 7

The unknowns are the amounts of the first and second brands.
x+y=320 (this is your equation for the amounts)
0.08x +0.13y=.11(320) (this is your equation for the concentrations)
We can use the substitution or elimination method to solve this.

Answer 8

Does that make sense?

Answer 9

no, im still trying to figure out how you got 8 and 13 from 9 and 14....it was a pretty good example though

Answer 10

still stuck on this problem ?

Answer 11

yes, still trying to figure out how 9 and 14 became 8 and 13

Answer 12

wait I have it. they gave me an example. if I substitute using my formulas is would be:

brand 1:240 ml
brand 2: 160 ml is that right
@ganeshie8 @ikram002p

Answer 13

not formulas...I meant values.

Answer 14

this is easy problem. lets work it from SCRATCH, real quick ok ?

Answer 15

u wid me ?

Answer 16

yes

Answer 17

say, he uses \(A\) mL from first brand, and \(B\) mL from second brand, then :

\(A + B = 400 \) ---------------(1)

Answer 18

since he wants it to be of \(11\%\) vinegar :

\(\large (9\%~ of ~A) + (14\%~ of ~B) = (11\%~ of ~400) \) ----------(2)

Answer 19

two equations, two unknowns. u can solve them.

Answer 20

let me knw if something doesnt make sense :)

Answer 21

im with you

Answer 22

I still have brand 1: 240
brand 2: 160
@ganeshie8

Answer 23

let me check

Answer 24

equation (2) becomes :
\(\large 0.09A + 0.14B = 0.11*400\)

Answer 25

solving them both gives :
\(\large A = 240,~~ B=160\)

http://www.wolframalpha.com/input/?i=A%2BB%3D400%2C+.09A+%2B+.14B%3D.11*400

Answer 26

Good job !! @AwesomeAries

Answer 27

Thank you @ganeshie8

Answer 28

np :)