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 $\$32$ for the meal, plus $\$4$ per pound for the lobster she picks. At the second restaurant, Amy would pay $\$2$ per pound for the lobster, in addition to $\$40$ 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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Solve a system of equations using any method: word problems

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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

for the meal, plus

\$4

per pound for the lobster she picks. At the second restaurant, Amy would pay

\$2

per pound for the lobster, in addition to

\$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.

Set up equations: Step $1$ : Set up equations based on the cost structure of each restaurant. $\newline$ First restaurant: Total cost = $\$32$ + $\$4$ per pound of lobster. $\newline$ Second restaurant: Total cost = $\$40$ + $\$2$ per pound of lobster. $\newline$ Let $x$ be the weight of the lobster in pounds, and $y$ be the total cost. $\newline$ Equation for first restaurant: $y = 4x + 32$ $\newline$ Equation for second restaurant: $y = 2x + 40$
Equate expressions for $x$ : Step $2$ : Equate the two expressions for $y$ to find $x$ . $4x + 32 = 2x + 40$ Subtract $2x$ from both sides: $2x + 32 = 40$ Subtract $32$ from both sides: $2x = 8$ Divide both sides by $2$ : $x = 4$
Substitute $x$ back: Step $3$ : Substitute $x = 4$ back into any of the original equations to find $y$ . Using $y = 4x + 32$ : $y = 4(4) + 32 = 16 + 32 = 48$