Answered

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How many gallons of a 42% salt solution do we need to mix with 98 gallons of a 20% salt solution so that the resulting mixture is a 28% salt solution ?

Sagot :

CrazyMoosen

Answer:

56

Step-by-step explanation:

98 gallons of a 20 percent salt solution results in 20/100 * 98 = 19.6 gallons of salt.

Let's say we need x gallons of the 42% salt solution.

To make sure that the resulting mixture has 28% salt, we need to have the total salt divided by the total amount of gallons.

We have 98 total gallons in the first solution, and x total gallons in the second solution. We have 19.6 gallons of salt in the first solution and 42% of x gallons in the second solution:

[tex]19.6+\frac{42}{100}(x)=\frac{28}{100}(98+x)[/tex]

Expanding, we have

[tex]19.6+\frac{42}{100}x=27.44+\frac{28}{100}x[/tex]

Subtracting 19.6 and subtracting 28/100x from both sides equals

[tex]\frac{14}{100}x=7.84[/tex]

Multiplying both sides by 100:

[tex]14x=784[/tex]

Dividing both sides by 14:

[tex]x=56[/tex]

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