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We're told that the total cost of filling up your car with

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gas varies directly with the number of gallons of gasoline

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you are purchasing.

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So this first statement tells us that if x is equal to the

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number of gallons purchased, and y is equal to the cost of

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filling up the car, this first statement tells us that y

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varies directly with the number of gallons, with x.

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So that means that y is equal to some constant, we'll just

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call that k, times x.

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This is what it means to vary directly.

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If x goes up, y will go up.

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We don't know what the rate is. k tells us the rate.

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If x goes down, y will be down.

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Now, they give us more information, and this will

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help us figure out what k is.

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If a gallon of gas costs $2.25, how many gallons could

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you purchase for $18?

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So if x is equal to 1-- this statement up here, a gallon of

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gas-- that tells us if we get 1 gallon, if x is equal to 1,

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then y is $2.25, right?

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y is what it costs.

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They tell us 1 gallon costs $2.25, so you could write it

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right here, $2.25 is equal to k times x, times 1.

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Well, I didn't even have to write the times 1 there.

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It's essentially telling us exactly what the

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rate is, what k is.

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We don't even have to write that 1 there.

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k is equal to 2.25.

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That's what this told us right there.

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So the equation, how y varies with x, is y is equal to

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2.25x, where x is the number of gallons we purchase.

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y is the cost of that purchase, so

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it's $2.25 a gallon.

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And then they ask us, how many gallons could you

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purchase for $18?

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So $18 is going to be our total cost. It is y cost of

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filling the car.

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So 18 is going to be equal to 2.25x.

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Now if we want to solve for x, we can divide both sides by

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2.25, so let's do that.

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You divide 18 by 2.25, divide 2.25x by 2.25,

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and what do we get?

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Let me scroll down a little bit.

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The right-hand side, the 2.25's cancel out, you get x.

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And then what is 18 divided by 2.25?

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So let me write this down.

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So first of all, I just like to think of it as a fraction.

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2.25 is the same thing-- let me write over here-- 2.25 is

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equal to 2 and 1/4, which is the same thing as 9 over 4.

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So 18 divided by 2.25 is equal to 18 divided by 9 over 4,

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which is equal to 18 times 4 over 9, or 18 over 1

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times 4 over 9.

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And let's see, 18 divided by 9 is 2, 9 divided by 9 is 1.

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That simplifies pretty nicely into 8.

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So 18 divided by 2.25 is 8, so we can buy 8 gallons for $18.

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