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

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Algebra 2

Write a linear inequality: word problems

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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

to cover the costs of the camp. Tickets for the crab dinner sell for

\$31

apiece. Those people who don't like crab can purchase the vegetarian dinner ticket for

\$21

each.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of crab dinners sold

\newline

y =

the number of alternative dinners sold

\newline

Choices:

\newline

(A)

21x + 31y \geq 1,100

\newline

(B)

31x + 21y \geq 1,100

\newline

(C)

31x + 21y > 1,100

\newline

(D)

21x + 31y > 1,100

Define Variables and Prices: Define the variables and the price for each type of dinner. $\newline$ We are given: $\newline$ Price of each crab dinner ticket: $\$31$ $\newline$ Number of crab dinner tickets sold: $x$ $\newline$ Price of each vegetarian dinner ticket: $\$21$ $\newline$ Number of vegetarian dinner tickets sold: $y$ $\newline$ We need to find the inequality that represents the total amount of money raised from selling these tickets, which must be at least $\$1,100$ .
Total Money from Crab Dinners: Write the expression for the total amount of money raised from selling crab dinner tickets. $\newline$ The total amount of money from crab dinners is the price of one crab dinner ticket times the number of crab dinner tickets sold. $\newline$ Total money from crab dinners = Price of crab dinner $\times$ Number of crab dinners sold $\newline$ = $\$(31) \times x$ $\newline$ = $31x$
Total Money from Vegetarian Dinners: Write the expression for the total amount of money raised from selling vegetarian dinner tickets. $\newline$ The total amount of money from vegetarian dinners is the price of one vegetarian dinner ticket times the number of vegetarian dinner tickets sold. $\newline$ Total money from vegetarian dinners = Price of vegetarian dinner $\times$ Number of vegetarian dinners sold $\newline$ = $\$21 \times y$ $\newline$ = $21y$
Combine Expressions for Total Money Raised: Combine the expressions to form the total amount of money raised from both types of dinners. $\newline$ The total amount of money raised is the sum of the money from crab dinners and the money from vegetarian dinners. $\newline$ Total money raised = Money from crab dinners + Money from vegetarian dinners $\newline$ = $31x + 21y$
Write Inequality for Total Money Raised: Write the inequality that represents the condition that the total amount of money raised must be at least $\$1,100$ . The troop needs to make at least $\$1,100$ , so the total money raised must be greater than or equal to $\$1,100$ . Inequality: $31x + 21y \geq 1,100$