Question 386243: A 400 gram solution is 25% salt. How much salt must be added to produce a solution that is 40% salt?
Found 2 solutions by gwendolyn, stanbon:
Answer by gwendolyn(128)   (Show Source):
You can put this solution on YOUR website! First of all, we'll determine our variables:
let x=grams of salt that you already have
let y=grams of salt that need to be added
let z=total amount of salt in the solution after adding salt
We know that salt makes up 25% of the 400g solution, and that 25% can also be written as .25. Thus, we can write an equation to determine x's value:
x=.25*400g
x=100g
Therefore, there are 100 grams of salt already in the solution.
Now that we've determined x's value, we'll bring z into the equation. There are two ways to calculate z. z is equivalent to the sum of x and y. Remember, x is equal to 100 grams. So, z's equation is as follows:
z=100g+y
The other way to calculate z is as a percentage of the final solution. As the question states, we want the final solution to have a salt content of 40% (which we can write as .40). The final amount of solution can be written as below:
400g+y=total amount of solution after adding salt.
This is because we are adding y (the amount of salt needed to bring the salt content to 40 percent)to the amount of solution which we already have.
Therefore, the second way to express z is below:
z=.40*(400g+y)
After we have two equations for z, we can set them equal to each other as follows:
100g+y=.40*(400g+y)
We then can distribute the .40 over the parenthesis.
100g+y=160g+.40y
And then we can subtract 100 grams from both sides of the equation.
y=60g+.40y
Next, we subtract .40 y from both sides of the equation to get y on one side.
.6y=60g
Finally, we can divide both sides by .6 to isolate y.
y=100g
Therefore, you must add 100g of salt to the solution to make it 40 percent salt.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! A 400 gram solution is 25% salt. How much salt must be added to produce a solution that is 40% salt?
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Quantity: x + y = 400
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Salt Eq:: 0.25x + y = 0.40*400
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Multiply Quantity thru by 25
Multiply Salt by 100
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25x + 25y = 25*400
25x + 100y = 40*400
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75y = 15*400
y = 80 gram (amt. of salt that must be added)
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Cheers,
Stan H.
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