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A scouting troop from Lowell is organizing a crab feed to raise money for camp. They need to make at least $1,100\$1,100 to cover the costs of the camp. Tickets for the crab dinner sell for $31\$31 apiece. Those people who don't like crab can purchase the vegetarian dinner ticket for $21\$21 each.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of crab dinners sold\newliney=y = the number of alternative dinners sold\newlineChoices:\newline(A) 21x+31y≥1,10021x + 31y \geq 1,100\newline(B) 31x+21y≥1,10031x + 21y \geq 1,100\newline(C) 31x + 21y > 1,100\newline(D) 21x + 31y > 1,100

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Q. A scouting troop from Lowell is organizing a crab feed to raise money for camp. They need to make at least $1,100\$1,100 to cover the costs of the camp. Tickets for the crab dinner sell for $31\$31 apiece. Those people who don't like crab can purchase the vegetarian dinner ticket for $21\$21 each.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of crab dinners sold\newliney=y = the number of alternative dinners sold\newlineChoices:\newline(A) 21x+31y≥1,10021x + 31y \geq 1,100\newline(B) 31x+21y≥1,10031x + 21y \geq 1,100\newline(C) 31x+21y>1,10031x + 21y > 1,100\newline(D) 21x+31y>1,10021x + 31y > 1,100
  1. Define Variables and Prices: Define the variables and the price for each type of dinner.\newlineWe are given:\newlinePrice of each crab dinner ticket: $31\$31\newlineNumber of crab dinner tickets sold: xx\newlinePrice of each vegetarian dinner ticket: $21\$21\newlineNumber of vegetarian dinner tickets sold: yy\newlineWe need to find the inequality that represents the total amount of money raised from selling these tickets, which must be at least $1,100\$1,100.
  2. Total Money from Crab Dinners: Write the expression for the total amount of money raised from selling crab dinner tickets.\newlineThe total amount of money from crab dinners is the price of one crab dinner ticket times the number of crab dinner tickets sold.\newlineTotal money from crab dinners = Price of crab dinner ×\times Number of crab dinners sold\newline= $(31)×x\$(31) \times x\newline= 31x31x
  3. Total Money from Vegetarian Dinners: Write the expression for the total amount of money raised from selling vegetarian dinner tickets.\newlineThe total amount of money from vegetarian dinners is the price of one vegetarian dinner ticket times the number of vegetarian dinner tickets sold.\newlineTotal money from vegetarian dinners = Price of vegetarian dinner ×\times Number of vegetarian dinners sold\newline= $21×y\$21 \times y\newline= 21y21y
  4. Combine Expressions for Total Money Raised: Combine the expressions to form the total amount of money raised from both types of dinners.\newlineThe total amount of money raised is the sum of the money from crab dinners and the money from vegetarian dinners.\newlineTotal money raised = Money from crab dinners + Money from vegetarian dinners\newline= 31x+21y31x + 21y
  5. Write Inequality for Total Money Raised: Write the inequality that represents the condition that the total amount of money raised must be at least $1,100\$1,100. The troop needs to make at least $1,100\$1,100, so the total money raised must be greater than or equal to $1,100\$1,100. Inequality: 31x+21y≥1,10031x + 21y \geq 1,100

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