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Aiden has $200 with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get 40 hats. If Aiden purchases only t-shirts, he will get 80t-shirts. Which of the following best models the relationship between the number of hats, h, and the number of t-shirts, t, that Aiden could purchase with this money? Choose 1 answer: (A) 40 h+80 t=400 (B) 80 h+40 t=200 (c) 5h+2.5 t=200 (D) 2.5 h+5t=200

Aiden has $200 \$ 200 with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get 4040 hats. If Aiden purchases only t t -shirts, he will get 80 80 t\mathrm{t} -shirts. Which of the following best models the relationship between the number of hats, h h , and the number of t \mathrm{t} -shirts, t t , that Aiden could purchase with this money?\newlineChoose 11 answer:\newline(A) 40h+80t=400 40 h+80 t=400 \newline(B) 80h+40t=200 80 h+40 t=200 \newline(C) 5h+2.5t=200 5 h+2.5 t=200 \newline(D) 2.5h+5t=200 2.5 h+5 t=200

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Q. Aiden has $200 \$ 200 with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get 4040 hats. If Aiden purchases only t t -shirts, he will get 80 80 t\mathrm{t} -shirts. Which of the following best models the relationship between the number of hats, h h , and the number of t \mathrm{t} -shirts, t t , that Aiden could purchase with this money?\newlineChoose 11 answer:\newline(A) 40h+80t=400 40 h+80 t=400 \newline(B) 80h+40t=200 80 h+40 t=200 \newline(C) 5h+2.5t=200 5 h+2.5 t=200 \newline(D) 2.5h+5t=200 2.5 h+5 t=200
  1. Determine cost of one hat: Let's first determine the cost of one hat. If Aiden can buy 4040 hats with $200\$200, then the cost of one hat is $200\$200 divided by 4040 hats.\newlineCalculation: $200/40\$200 / 40 hats = $5\$5 per hat
  2. Determine cost of one t-shirt: Now, let's determine the cost of one t-shirt. If Aiden can buy 8080 t-shirts with $200\$200, then the cost of one t-shirt is $200\$200 divided by 8080 t-shirts.\newlineCalculation: $200/80\$200 / 80 t-shirts = $2.50\$2.50 per t-shirt
  3. Express relationship between hats and t-shirts: We need to express the relationship between the number of hats hh and t-shirts tt that Aiden can buy with $200\$200. Since each hat costs $5\$5 and each t-shirt costs $2.50\$2.50, the total cost when Aiden buys hh hats and tt t-shirts would be 5h+2.5t5h + 2.5t.
  4. Model the equation: The total amount Aiden can spend is $200\$200, so the equation that models the relationship between the number of hats hh and t-shirts tt is 5h+2.5t=2005h + 2.5t = 200.
  5. Match equation with choices: Now, let's match our equation with the given choices. The correct equation is 5h+2.5t=2005h + 2.5t = 200, which corresponds to choice (C)(C).

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