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]
