SOLUTION: A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 16% vinegar. The chef wants to make 210 milliliters of a mixture that contains 48% vinegar. Ho
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Question 1138072: A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 16% vinegar. The chef wants to make 210 milliliters of a mixture that contains 48% vinegar. How much vinegar and how much Italian dressing should she use? Found 2 solutions by josmiceli, ikleyn:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Let = ml of 100% vinegar needed
Let = ml of Italian dressing needed
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(1)
(2)
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(2)
(2)
(2)
and
(1)
Subtract (1) from (2)
(2)
(1)
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and
(1)
(1)
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80 ml of 100% vinegar are needed
130 ml of Italian dressing are needed
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check:
(2)
(2)
(2)
(2)
OK
In this problem, the concentration is the ratio of the vinegar volume to the total volume of the dressing.
Let x be the volume of the 16% Italian dressing and y be the volume of the 100% vinegar.
Then from the condition, you have these two equations
x + y = 210 milliliters (1) (total volume) and
0.16x + y = 0.48*210 milliliters (2) (the volume of the 100% vinegar)
To solve the sytem, subtract equation (2) from equation (1). In this way you eliminate y and obtain single equation for x
x - 0.16x = 210 - 0.48*210
(1 - 0.16)*x = 210 - 0.48*210
x = = 130.
ANSWER. The chef should mix 130 mL of the 16% Italian vinegar with (210-130) = 80 mL of the 100% vinegar.
CHECK. 0.16*130 + 80 = 100.8 mL of the 100% vinegar = 0.48*210 mL. ! Correct !
You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, from very detailed to very short.
Read them and become an expert in solution mixture word problems.
