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At the gas station, gas usually costs $3. This month, there's a sale: for every drink you purchase you save $0.20 on gas. Assuming your sale savings are less than the cost of your gas, are your total savings on gas proportional to the number of drinks you purchase? Choose 1 answer: (A) Yes (B) No

At the gas station, gas usually costs $3 \$ 3 . This month, there's a sale: for every drink you purchase you save $0.20 \$ 0.20 on gas.\newlineAssuming your sale savings are less than the cost of your gas, are your total savings on gas proportional to the number of drinks you purchase?\newlineChoose 11 answer:\newline(A) Yes\newline(B) No

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Q. At the gas station, gas usually costs $3 \$ 3 . This month, there's a sale: for every drink you purchase you save $0.20 \$ 0.20 on gas.\newlineAssuming your sale savings are less than the cost of your gas, are your total savings on gas proportional to the number of drinks you purchase?\newlineChoose 11 answer:\newline(A) Yes\newline(B) No
  1. Understand Proportionality Definition: To determine if the savings on gas are proportional to the number of drinks purchased, we need to understand the definition of proportionality. Proportionality means that as one quantity increases, the other quantity increases at a constant rate. In this case, we are looking at the relationship between the number of drinks purchased and the savings on gas.
  2. Denote Variables and Calculate Total Savings: Let's denote the number of drinks purchased as d d and the savings on gas per drink as s s . The total savings on gas, T T , can be calculated by multiplying the number of drinks by the savings per drink: T=d×s T = d \times s .
  3. Substitute Savings Per Drink Value: Given that the savings per drink is \(0\).\(20\), we can substitute \( s \) with 00.2020 in the equation: T=d×0.20 T = d \times 0.20 .
  4. Total Savings Directly Proportional to Drinks: This equation shows that the total savings on gas, T T , is directly proportional to the number of drinks purchased, d d , because the savings per drink, s s , is a constant value (\(0\).\(20\)). Therefore, as the number of drinks increases, the total savings on gas also increases at a constant rate of 00.2020 per drink.
  5. Conclusion: Savings Proportional to Drinks: Since the relationship between the number of drinks purchased and the total savings on gas is a direct proportion, the answer to the question is (A)(A) Yes.

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