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Video: Deciding Whether Two Quantities Are in a Directly Proportional Relationship

Kathryn Kingham

A gas station charges $3 per gallon for gasoline, and $6 for a car wash. Carl never washes his car there because he thinks it is too expensive, but he often buys gasoline there. Is the total money he spends at the station directly proportional to the amount of gasoline he buys?

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Video Transcript

A gas station charges three dollars per gallon for gasoline, and six dollars for car wash. Daniel never washes his car there because he thinks it is too expensive, but he often buys gasoline there. Is the total money he spends at the station directly proportional to the amount of gasoline he buys?

I guess first, we need to remember what directly proportional means. In things that are directly proportional, as one amount increases, another amount increases at the same rate. In our problem, we wanna know the total money spent, the total money that Daniel spends, is that directly proportional to the gas that he buys.

The total money that Daniel spends is what Daniel buys multiplied by how much that costs. Daniel buys gasoline and he pays three dollars per gallon of gasoline that he buys. And as the amount of gasoline he buys goes up, the money that Daniel spends goes up at the same rate. It increases by three dollars for every gallon that he buys.

The answer to this question is: Yes. The total money that Daniel spends is directly proportional to the amount of gasoline that he buys because Daniel only buys gas there. He does not buy a car wash.