Algebra

Direct variation 1 | Rational expressions | Algebra II | Khan Academy

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We are given that the total cost of refueling our car, is directly proportional to how many gallons of gasoline we will buy. Using the first statement, we denote by x – x = the number of gallons purchased, and y will denote – y = the cost of charging the car. In the first statement we are given, that there is a proportional relationship between y and the number of gallons, which are x. This means that y is equal to a constant, we will denote it by k, and we will multiply by x (y = k.x). This is a proportional relationship. If x increases, then y will also increase. We do not know what the value is, but it becomes clear to us. If x decreases, the same will happen with y. Here we are given a little more information, which will help us understand what k is. If a gallon of gasoline costs $ 2.25, then how many gallons can you buy for $ 18? If x = 1 – the statement here above for one gallon of gasoline, which says that if we have one gallon and x = 1, then y = 2.25, right? y is the amount for gasoline. We’ve been told that 1 gallon costs $ 2.25, so I’ll write it down here 2.25 = k.1 I didn’t even have to write multiplied by 1 there. It clearly shows us exactly what is the value, how much is k. We don’t even have to write 1 there. k = 2.25 This is given to us here. So the equation for the relationship between x and y is y = 2.25x, where x is the number of gallons we will buy. y is the value of the purchase, at $ 2.25 per gallon. Looking for how many gallons we can to buy for 18 dollars? $ 18 will be the value of the entire purchase. This is y, y is the cost of refueling. So 18 = 2.25x To find x, we divide the two sides by 2.25, let’s do it. Divide 18 by 2.25, divide 2.25x by 2.25, and what do we get? I’ll go a little further down. On the right 2.25 is shortened and remains x. And how much is 18 / 2.25? I will write it here. Let’s look at it as a liver. 2.25 is the same – just to write it here – 2.25 = 2 and 1/4, which is the same as 9/4 In other words 18 / 2.25 = 18 / (9/4), which is equal to 18x (4/9), or 18/1 x 4/9. Let’s see, 18/9 = 2, 9/9 = 1 And after simplification we get 8. 18 / 2.25 = 8, so we can buy 8 gallons for $ 18.

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