How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution?
A. 0.50
B. 0.67
C. 1.00
D. 1.50
E. 2.00
The OA is A.
Let the number of gallons of water to be added
(concentration of A)*(Volume of A)+(concentration of B)*(Volume of B) = (desired concentration in resultant mixture)*(Volume of resultant mixture = A+B)
Water has a salt concentration of 0
(0.15)*(1) + (0)*(x) = (0.1)*(1+x)
0.15 = 0.1 + 0.1x
0.05 = 0.1x
0.05/0.1 = x --> x = 0.5.
Has anyone another approach to solve this PS question? Regards!
How many gallons of water must be mixed with 1 gallon
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Let x = the volume (in gallons) of water that must be added to the existing mixture.AAPL wrote:How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution?
A. 0.50
B. 0.67
C. 1.00
D. 1.50
E. 2.00
We have 1 gallon of the EXISTING mixture, which is 15% salt.
15% of 1 = 0.15
So, the EXISTING mixture contains 0.15 gallons of salt
When we add x gallons of water to the existing mixture, the NEW mixture has a volume of 1 + x gallons
We want the NEW mixture to contain 10% salt
So, we want (salt volume)/(TOTAL volume) to equal 10%
In other words, we want: (0.15)/(1 + x) = 1/10
Cross multiply to get: (10)(0.15) = (1)(1 + x)
Simplify: 1.5 = 1 + x
Solve to get: x = 0.5
Answer: A
Cheers,
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Amount of salt = 15% of 1 gallon = 0.15 gallon.AAPL wrote:How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution?
A. 0.50
B. 0.67
C. 1.00
D. 1.50
E. 2.00
We can PLUG IN THE ANSWERS, which represent the amount of water that must be added to reduce the salt concentration to 10%.
B: 2/3 gallon
Salt concentration = (amount of salt)/(new total volume) = 0.15/(1 + 2/3) = 0.15/(5/3) = (0.15 * 3)/5 = (15*3)/500 = (3*3)/100 = 9/100 = 9%.
The salt concentration is TOO LOW.
To increase the salt concentration, we must add LESS WATER.
The correct answer is A.
A: 0.5 gallon
Salt concentration = (amount of salt)/(new total volume) = 0.15/(1 + 0.5) = 0.15/1.5= 15/150 = 1/10 = 10%.
Success!
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Salt percentage in the original solution: 15%.AAPL wrote:How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution?
A. 0.50
B. 0.67
C. 1.00
D. 1.50
E. 2.00
Salt percentage in the added water: 0%.
Salt percentage in the mixture: 10%.
Let S = the original solution and W = the added water.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the two starting percentages (15% and 0%) on the ends and the goal percentage (10%) in the middle.
S 15%------------10%--------------0% W
Step 2: Calculate the distances between the percentages.
S 15%-----5-----10%-----10-----0% W
Step 3: Determine the ratio in the mixture.
The required ratio of original solution to added water is equal to the RECIPROCAL of the distances in red.
S:W = 10:5 = 1 : 0.5.
The ratio in blue indicates that the 1 gallon of original solution must be combined with 0.5 gallon of pure water.
The correct answer is A.
For two similar problems, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.html
An alternate approach:
In the original solution, the amount of salt = 0.15(1) = 0.15 gallon.
After the water is added, the 0.15 gallon of salt must constitute 10% of the final mixture:
0.15= 0.1x
15 = 10x.
x = 15/10 = 1.5 gallons.
Since the volume of the final mixture is 1.5 gallons, and the volume of the original solution is 1 gallon, the volume of the added water = 1.5 - 1 = 0.5 gallon.
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The initial solution has 0.15 gallons salt. We can let w = the number of gallons of water needed to be added to obtain a 10% salt solution and create the equation:AAPL wrote:How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution?
A. 0.50
B. 0.67
C. 1.00
D. 1.50
E. 2.00
0.15/(1 + w) = 1/10
1.5 = 1 + w
0.5 = w
Answer: A
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