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Susan set up a lemonade stand to raise money for a children's hospital. She's selling cups of lemonade for 2.502.50 $\$ each and brownies for 1.501.50 $\$ each. She sells 280280 items and raises 540540 $\$. This system of equations can be used to represent the situation:\newlinex+y=280x + y = 280\newline2.5x+1.5y=5402.5x + 1.5y = 540\newlineWhich statement is correct?\newline(A) In the system of equations, xx represents the amount of money Susan raises from selling brownies, and $\$00 represents the amount of money she raises from selling lemonade.\newline(B) In the system of equations, xx represents the number of brownies Susan sells, and $\$00 represents the number of cups of lemonade she sells.\newline(C) In the system of equations, xx represents the number of cups of lemonade Susan sells, and $\$00 represents the number of brownies she sells.\newline(D) In the system of equations, xx represents the amount of money Susan raises from selling lemonade, and $\$00 represents the amount of money she raises from selling brownies.\newlineHow much money does Susan raise from selling lemonade?\newline$\$____

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Q. Susan set up a lemonade stand to raise money for a children's hospital. She's selling cups of lemonade for 2.502.50 $\$ each and brownies for 1.501.50 $\$ each. She sells 280280 items and raises 540540 $\$. This system of equations can be used to represent the situation:\newlinex+y=280x + y = 280\newline2.5x+1.5y=5402.5x + 1.5y = 540\newlineWhich statement is correct?\newline(A) In the system of equations, xx represents the amount of money Susan raises from selling brownies, and $\$00 represents the amount of money she raises from selling lemonade.\newline(B) In the system of equations, xx represents the number of brownies Susan sells, and $\$00 represents the number of cups of lemonade she sells.\newline(C) In the system of equations, xx represents the number of cups of lemonade Susan sells, and $\$00 represents the number of brownies she sells.\newline(D) In the system of equations, xx represents the amount of money Susan raises from selling lemonade, and $\$00 represents the amount of money she raises from selling brownies.\newlineHow much money does Susan raise from selling lemonade?\newline$\$____
  1. Identify Variables: First, let's identify what xx and yy represent in the system of equations. The correct choice is (C) where xx represents the number of cups of lemonade Susan sells, and yy represents the number of brownies she sells.
  2. Solve First Equation: Now, let's solve the system of equations to find the values of xx and yy. Start with the first equation:\newlinex+y=280x + y = 280.
  3. Substitute xx into Second Equation: Substitute xx from the first equation into the second equation:\newline2.5x+1.5y=5402.5x + 1.5y = 540.\newlineReplace xx with (280y)(280 - y):\newline2.5(280y)+1.5y=5402.5(280 - y) + 1.5y = 540.
  4. Solve for y: Simplify and solve for y:\newline7002.5y+1.5y=540700 - 2.5y + 1.5y = 540,\newline700y=540700 - y = 540,\newliney=700540y = 700 - 540,\newliney=160y = 160.
  5. Substitute yy into First Equation: Substitute yy back into the first equation to find xx:x+160=280,x + 160 = 280,x=280160,x = 280 - 160,x=120.x = 120.
  6. Calculate Lemonade Revenue: Now, calculate the amount of money raised from selling lemonade. Since xx represents the number of cups of lemonade sold, and each cup costs $2.50\$2.50:Money from lemonade=2.50×120=300inlinelatex2.\text{Money from lemonade} = 2.50 \times 120 = 300inline_latex_2.

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