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# Writing proportional equations

Writing an equation to describe the relationship between the number of scoops in an ice cream cone and the price. Created by Sal Khan.

Video transcript

I scream, you scream, we all scream for ice cream! The following table describes the relationship between the number of scoops in an ice cream cone represented by x So this is the number of scoops in an ice cream cone, so that is x. And the price of the cone, represented by y. I'll do y in purple. Write the equation that describes this relationship. So let's see. When x is zero, y is zero. When x is 1, y is 1 3/4. Let me write this as an improper fraction so we can visualise it better. So this is 4/4 plus 3/4 which is equal to 7/4. When x = 2, y = 3 1/2. Let me see if I can write this in a clearer way. So this is 2 * 3 = 6 plus 1 is 7, so this is 7/2, which is the same as 14/4. And here we have when x = 3, y = 5 1/4 which I would write as an improper fraction 4 * 5 = 20, plus 1 = 21 so this is equal to 21/4. And then finally, if we'd write this as something over 4, this is equal to 28/4. 7 is the same thing as 28/4. So you see that this is a proportional relationship. The ratio between y and x let me write this The ratio between y and x is always equal to 7/4. Notice: here y is 7/4s of x, here: y is 7/4s of x it is a bigger number or you could say 1 and 3/4 of x Let me make that clear. So y/x = 7/4 Or we could say that y is always 7/4 of x. We could multiply both sides by x if we like. If we multiply both sides by x, we get y = 7/4 times x. You see that here, when x = 4, 7/4 * 4 = 7 When x is 0, y is 0. When x is 3, 7/4 times 3 is 21/4. which is the same thing as 5 1/4. So there we go. Let me input it just to make sure that we can input it right. y is equal to 7/4 x Let me get my... So we would just write y = 7/4 times x and let's check our answer. We got it right.