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Jimmy receives his first 3 video games free then pays $50 for each game after that. Is the amount of money he spends on video games proportional to the number of games he owns? Choose 1 answer: (A) Yes (B) No

Jimmy receives his first 33 video games free then pays $50 \$ 50 for each game after that.\newlineIs the amount of money he spends on video games proportional to the number of games he owns?\newlineChoose 11 answer:\newline(A) Yes\newline(B) No

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Q. Jimmy receives his first 33 video games free then pays $50 \$ 50 for each game after that.\newlineIs the amount of money he spends on video games proportional to the number of games he owns?\newlineChoose 11 answer:\newline(A) Yes\newline(B) No
  1. Define Variables: Let's define the variables:\newline- Let xx be the number of video games Jimmy owns.\newline- Let yy be the amount of money Jimmy spends on video games.\newlineAccording to the problem, Jimmy receives his first 33 video games for free. This means that for x=3x = 3, y=0y = 0. After that, for each additional game, he pays $50\$50. This means that for every game beyond the first 33, the cost increases by $50\$50.\newlineTo determine if the relationship is proportional, we need to see if there is a constant rate of change between xx and yy. A proportional relationship would mean that for every increase in xx, there is a constant increase in yy.\newlineLet's calculate the cost for the 44th game:\newlineFor yy22, Jimmy has to pay for yy33 game, so yy44.\newlineNow, let's calculate the cost for the 55th game:\newlineFor yy55, Jimmy has to pay for yy66 games, so yy77.\newlineWe can see that the amount Jimmy pays does not increase by a constant amount for each additional game because the first 33 games are free. The relationship between the number of games and the amount spent is not constant from the start; it only becomes constant after the first 33 games.
  2. Calculate Costs: To further illustrate why this is not a proportional relationship, let's consider the definition of a proportional relationship. A proportional relationship is one where the ratio of one quantity to the other is constant. In this case, the ratio of the amount spent to the number of games owned should be constant if the relationship is proportional.\newlineFor the first 33 games, the ratio y/xy/x would be 0/3=00/3 = 0. For the 44th game, the ratio would be 50/450/4. For the 55th game, the ratio would be 100/5=20100/5 = 20. The ratios are not the same, which means the relationship is not proportional.

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