A tank has a capacity of 10 gallons. When it is full, it contains 15%

Solution:

We see that currently there are 1.5 gallons of alcohol in the 10-gallon solution. Let x be the number of gallons of an 80% alcohol solution needed to replace the 15% alcohol solution to yield a 70% alcohol solution. So 0.15x gallons of alcohol from the original solution will be removed and 0.8x gallons of alcohol from the new solution will be added. We can create the equation:

(1.5 - 0.15x + 0.8x)/10 = 70/100

(1.5 + 0.65x)/10 = 7/10

1.5 + 0.65x = 7

0.65x = 5.5

x = 5.5/0.65 = 550/65 = 110/13

Alternate Solution:

We have 10 gallons of a 15% solution. From the 10 gallons, we will remove x gallons of this 15% solution and replace the removed solution with x gallons of 80% solution, and the result will be 10 gallons of a 70% solution. We can summarize these actions in the following equation:

10 (0.15) - x (0.15) + x (0.80) = 10 (0.70)

Now, let’s solve for x.

1.5 - 0.15x + 0.80x = 7

0.65x = 5.5

65x = 550

x = 550/65 = 110/13 gallons


Answer: B

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