How many gallons of pure water should be evaporated from 160 gallons of a solution containing 12% salt so that the remaining solution contains 20% salt?
Answers
The quantity of pure water is 64 gallons which are to be evaporated.
What is an expression?
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The total amount of salt must be equal before and after evaporation.
Multiply the percent of salt in the solution before evaporation by the total gallons of solution
= 12% x 160 gallons convert 12% to decimal form (12% ÷ 100)
= 0.12 * 60
Subtract the number of gallons of pure water that should be evaporated from the total number of gallons of the solution and multiply by the percent of salt in the solution after evaporation
= 20% * (160 - x)convert 20% to decimal form (20% ÷ 100)
= 0.20(160 - x)
Set the before & after evaporation equations equal to one another to solve for x.
0.12 x 160 = 0.20(160 - x)
19.2 = (0.20 * 160) + (0.20 * -x)
19.2 = 32 - 0.20x
-12.8 = -0.20x
64 gallons = x
Therefore, the quantity of pure water is 64 gallons which are to be evaporated.
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The total amount of salt must be equal before and after evaporation.
STEP 1
BEFORE EVAPORATION: multiply the percent of salt in the solution before evaporation by the total gallons of solution
= 12% * 160 gallonsconvert 12% to decimal form (12% ÷ 100)
= 0.12 * 60
STEP 2
AFTER EVAPORATION: subtract the number of gallons of pure water that should be evaporated from the total number of gallons of the solution and multiply by the percent of salt in the solution after evaporation
= 20% * (160 - x)convert 20% to decimal form (20% ÷ 100)
= 0.20(160 - x)
STEP 3
Set the before & after evaporation equations equal to one another to solve for x.
0.12 * 160= 0.20(160 - x)multiply 0.20 by each term in parentheses
19.2= (0.20 * 160) + (0.20 * -x)multiply in parentheses
19.2 = 32 - 0.20xsubtract 32 from both sides
-12.8= -0.20xdivide both sides by -0.20
64 gallons= x
CHECK:substitute x= 64 into the step 3 equation
0.12 * 160= 0.20(160 - x)19.2= 0.20(160 - 64)subtract in parentheses19.2= 0.20(96)19.2= 19.2
ANSWER: 64 gallons of pure water should be evaporated.
Hope this helps! :)
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I need help with this question!
Answers
The rule of multiplying fractions is change the division sign into multiplication and change the second fraction into it's reciprocal.
9/2 x 4/3
2 x 3 = 6
9 x 4 = 36
36/6= 6
in conclusion 4 1/2 x 3/4 = 6
Final answer:
To divide 4 1/2 by 3/4, convert 4 1/2 to the improper fraction 9/2. Then, multiply it by the reciprocal of 3/4. The result is 6.
Explanation:
To divide a mixed number by a fraction, we first need to convert the mixed number to an improper fraction. In this case, 4 1/2 can be written as the improper fraction 9/2. Then, we can multiply the numerator of the first fraction (9/2) by the reciprocal of the second fraction (4/3).
So, 4 1/2 ÷ 3/4 = (9/2) × (4/3) = 36/6 = 6.
Therefore, 4 1/2 ÷ 3/4 equals 6.
Learn more about Division of mixed numbers here:
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Answers
Answer:
X+1=3
x = 3 - 1
x = 2
Check:
2 + 1 = 3
x-4=5
x = 5 + 4
x = 9
Check:
9 - 4 = 5
Answer:
1)x=2
2)x=9
Step-by-step explanation:
x+1=3
=>x=3-1
therefore
x=2
second question
x-4=5
=>x=5+4
therefore
x=9
Answers
=LCM OF DENOMINATORS
=90
=60+75+72/90
=207/90
=2.3
Answers
Answer:
182
Step-by-step explanation:
225+67-110
Answer:
Step-by-step explanation:
Answers
Answer: 496.37
Step-by-step explanation:
If x represents time, the average rate of change of the function f(x) in the first three seconds is ___.
Answer for Blank 1:
Answers
(0,150) and (3,0)
We can easily solve for the slope.
m = (y2 - y1) / (x2 - x1)
m = (0 - 150) / (3 - 0) = -50
Therefore, the average rate of change of the function in the three seconds is -50.
Answer:
-50
Step-by-step explanation:
The rate of change formula = f(b) - f(a) / b - a
f(b) = the end number (so basically 0 becuase the line ends on the point (3, 0))
f(a) = the start number (so basically 150 becuase the line starts on the point (0, 150)
b = the end time (so basically 3 becuase the line ends on the point (3, 0))
a = the start time (so basically 0 becuase the line starts on the point (0, 150)
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sorry if that is confusing... moving on...
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You would apply these numbers = 0 - 150 / 3 - 0 = -150 / 3 = -50
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This is your rate of change
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I hope this helped :)