Question 100245
Let x be the capacity of the tank.
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The first time you fill it up you pump in 1/2 of x which in decimal form is 0.5x. The next time 
you fill it up you pump in 3/4 of x which in decimal form is 0.75x. Together these two fill-ups 
total 18 & 1/2 gallons or in decimal form 18.5 gallons. Write this in equation 
form:
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0.5x + 0.75x = 18.5
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Add the two terms on the left side and the equation becomes:
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1.25x = 18.5
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Solve for x by dividing both sides of this equation by 1.25 to get:
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x = 18.5/1.25 = 14.8 gallons
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So the tank holds about 14.8 gallons when full.
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The only reason I converted to decimal form was to avoid working with fractions. You could 
have just as well done this problem by working it in fraction form, starting with the
equation:
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{{{(1/2)x + (3/4)x = 37/2}}}
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where {{{37/2}}} is the improper fraction form of 18 1/2
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You could now get rid of the denominators by multiplying both sides of this equation (all
terms) by 4 to convert the equation to:
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2x + 3x = 74
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Adding the two terms on the left side results in:
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5x = 74
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and dividing both sides by 5 gives you the answer:
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x = 14 4/5
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and since 4/5 is equivalent to 8/10, this answer is also 14.8 gallons.
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Hope this helps you to understand the problem a little better.
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