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Define your variables and set up a system of equations, then solve. Round your answer to the nearest tenth.A 4% salt solution is mixed with an 14 % salt solution. How many grams of 14% salt solution need to be used to obtain 990 grams of a 10% solution?

User Magofoco
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1 Answer

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EXPLANATION

Assuming that x represents the number of grams of 4% of salt solutions and y represents the number of grams of 14% of salt solution used, we can apply the following relationship:

(1) x + y = 990 //This is because the total required weight is 990 grams

As the weight of salt in the 12% final salt solution is equal to the sum of each amount of salt, we can use the following equation:

(2) x*4/100 + y*14/100 = 12/100 * 999

Simplifying:

0.04x + 0.14y = 119.88

Isolating y from (1):

y = 990 - x

Substituting in (2):

0.04x + 0.14(990-x) = 119.88

Applying the distributive property:

0.04x + 138.6 - 0.14x = 119.88

Adding like terms:

-0.1x + 138.6 = 119.88

Subtracting -138.6 to both sides:

-0.1x = 119.88-138.6

Subtracting like numbers:

-0.1x = -18.72

Dividing both sides by -0.1:

x = -18.72/-0.1

Simplifying:

x = 187.2

Substituting x in (1):

(1) 187.2 + y = 990

Subtracting 187.2 to both sides:

y = 990 - 187.2

Subtracting like numbers:

y = 802.8

In conclusion, the amount of grams of each solution is as follows:

4% salt solution --------> 187.2 grams

14% salt solution --------> 802.8 grams

User Orustammanapov
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