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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Amy is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $32\$32 for the meal, plus $4\$4 per pound for the lobster she picks. At the second restaurant, Amy would pay $2\$2 per pound for the lobster, in addition to $40\$40 for the meal. Amy realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Amy pay for her dinner? What is the weight? Dinner would cost $\$ at either restaurant if Amy's lobster weighed pounds.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Amy is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $32\$32 for the meal, plus $4\$4 per pound for the lobster she picks. At the second restaurant, Amy would pay $2\$2 per pound for the lobster, in addition to $40\$40 for the meal. Amy realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Amy pay for her dinner? What is the weight? Dinner would cost $\$ at either restaurant if Amy's lobster weighed pounds.
  1. Set up equations: Step 11: Set up equations based on the cost structure of each restaurant.\newlineFirst restaurant: Total cost = $32\$32 + $4\$4 per pound of lobster.\newlineSecond restaurant: Total cost = $40\$40 + $2\$2 per pound of lobster.\newlineLet xx be the weight of the lobster in pounds, and yy be the total cost.\newlineEquation for first restaurant: y=4x+32y = 4x + 32\newlineEquation for second restaurant: y=2x+40y = 2x + 40
  2. Equate expressions for xx: Step 22: Equate the two expressions for yy to find xx.4x+32=2x+404x + 32 = 2x + 40Subtract 2x2x from both sides: 2x+32=402x + 32 = 40Subtract 3232 from both sides: 2x=82x = 8Divide both sides by 22: x=4x = 4
  3. Substitute xx back: Step 33: Substitute x=4x = 4 back into any of the original equations to find yy. Using y=4x+32y = 4x + 32: y=4(4)+32=16+32=48y = 4(4) + 32 = 16 + 32 = 48

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