# Video: Verifying Whether Two Quantities Are in a Proportional Relationship

Last week, Olivia bought one gallon of milk for \$3.50. This week, she bought 2 gallons of milk for \$7.50. Is the total money she paid proportional to the number of gallons?

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### Video Transcript

Last week, Olivia bought one gallon of milk for three dollars 50. This week, she bought two gallons of milk for seven dollars 50. Is the total money she paid proportional to the number of gallons?

So what we need to think about is this word here “proportional” cause we has to decide “is the total money she paid proportional to the number of gallons?” So if it is to be proportional and we have one gallon is equal to three dollars 50, then if we wanted two gallons, the price should be double. If we wanted four gallons, the price should be multiplied by four. So let’s see if that’s the case.

Well, if we’ve got one gallon for three dollars 50 and we want two gallons, then what we need to do is multiply each side of the equation by two. So one multiplied by two gives us two gallons. Then, we have to multiply three dollars 50 by two. Well, if we multiply three dollars 50 by two, we’re gonna get seven dollars. We can do that with some mental arithmetic because if we multiply three by two, that will give us six. And if we multiply 50 cents by two, that will give us one dollar. So six dollars plus one dollar gives us seven dollars.

However, this wasn’t the price that Olivia paid because Olivia bought two gallons of milk for seven dollars 50. So therefore, we can say and answer the question “the relationship is not proportional.”

So the total money she paid is not proportional to the number of gallons, because if it was, two gallons should have cost seven dollars. However, two gallons cost seven dollars 50.