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 240 milliliters of a dressing that is 12% vinegar. How much of each brand should she use?

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 240  milliliters of a dressing that is  12% vinegar. How much of each brand should she use?

anonymous · Answer

@dpaInc thank you

anonymous · Answer

there is going to be two different ammounts one for the first brand and another for the second

kropot72 · Answer

Amount of vinegar in final dressing = 240 * 0.12 mL
0.09A + 0.14B = 28.8..................(1)
A + B = 240.................................(2)
Where A and B are the amounts of the two brands.
Using (1) and (2) solve for A and B

mertsj · Answer

Let x = amount of 9% dressing to use. 
Then 240-x  amount of 14% dressing to use.
.09x+.14(240-x)=.12(240)

anonymous · Answer

so how exactly do i find the second one again?

anonymous · Answer

can i set 1 and 2 equal to eachother

kropot72 · Answer

No. What you do is to find an Equation for A and sustitute.
A = 240 - B
0.09(240 - B) + 0.14B = 28.8
21.6 - 0.09B + 0.14B = 28.8
0.05B = 7.2
Can you find B now?

mertsj · Answer

9x+14(240-x)=12(240)
9x+3360-14x=2880
-5x=-480
x=96=amount of 9% dressing to use
240-x=144= amount of 14% dressing to use

kropot72 · Answer

*substitute

kropot72 · Answer

Basically the method used by @Mertsj is an accelerated version of my method. Both methods give the correct answers when correctly used.

anonymous · Answer

ok so i got for the first one 28.8 
and the second one i got 144

anonymous · Answer

did i use the methods correctly?

kropot72 · Answer

No. The correct answers are 144 mL and 96 mL

anonymous · Answer

dangit

anonymous · Answer

144 belongs to the second dressin right

kropot72 · Answer

You correctly got 144 mL for the amount of one of the brands of dressing. Allyou need to do is to subtract 144 from the final amount of the mixture of dressings to find the amount of the other brand of dressing.
240 - 144 = ? mL

anonymous · Answer

96

kropot72 · Answer

You got it :) 96 mL

anonymous · Answer

so once again i ask 144 belongs to the first dressing 96

anonymous · Answer

belongs to the second

kropot72 · Answer

96 mL of the 9% vinegar dressing and 144 mL of the 14% vinegar dressing are the .correct allocations

anonymous · Answer

once again thanks for the help