SOLUTION: you fill your car's gas tank when it is about 1/2 empty. The next week, you fill the tank a second time when it is about 3/4 empty. If you buy a total of 18 1/2 gallons of gas on t

Algebra ->  Equations -> SOLUTION: you fill your car's gas tank when it is about 1/2 empty. The next week, you fill the tank a second time when it is about 3/4 empty. If you buy a total of 18 1/2 gallons of gas on t      Log On


   

Question 100245This question is from textbook
: you fill your car's gas tank when it is about 1/2 empty. The next week, you fill the tank a second time when it is about 3/4 empty. If you buy a total of 18 1/2 gallons of gas on these two days, about how many gallons does the tank hold? This question is from textbook

Found 2 solutions by ptaylor, bucky:
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the number of gallons that the full tank holds
The first time you fill it, you put (1/2)x gallons in
The second time you fill it, you put (3/4)x gallons in
Now we are told that (1/2)x+(3/4)x=18.5 gal or
(5/4)x=18.5 gal multiply both sides by 4
5x=74 divide both sides by 5
x=14.8 gal-----------------------------number of gal the tank holds
CK
(1/2)*14.8+(3/4)*14.8=18.5
7.4+11.1=18.5
18.5=18.5

Hope this helps----ptaylor

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the capacity of the tank.
.
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
.
Add the two terms on the left side and the equation becomes:
.
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
.
So the tank holds about 14.8 gallons when full.
.
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:
.
%281%2F2%29x+%2B+%283%2F4%29x+=+37%2F2
.
where 37%2F2 is the improper fraction form of 18 1/2
.
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:
.
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.
.
Hope this helps you to understand the problem a little better.
.