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A candidate running for office is putting on a gala as a fundraiser, with hopes of raising more than $\$7,200$ in political contributions. Single tickets cost $\$31$ , while an entire table can be reserved for $\$640$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of single tickets sold $\newline$ $y =$ the number of tables sold $\newline$ Choices: $\newline$ (A) $640x + 31y > 7,200$ $\newline$ (B) $31 + x + 640 + y > 7,200$ $\newline$ (C) $640 + x + 31 + y > 7,200$ $\newline$ (D) $31x + 640y > 7,200$

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Write a linear inequality: word problems

Full solution

Q. A candidate running for office is putting on a gala as a fundraiser, with hopes of raising more than

\$7,200

in political contributions. Single tickets cost

\$31

, while an entire table can be reserved for

\$640

.

\newline

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

\newline

x =

the number of single tickets sold

\newline

y =

the number of tables sold

\newline

Choices:

\newline

(A)

640x + 31y > 7,200

\newline

(B)

31 + x + 640 + y > 7,200

\newline

(C)

640 + x + 31 + y > 7,200

\newline

(D)

31x + 640y > 7,200

Calculate Single Ticket Revenue: Determine the cost of a single ticket and the number of single tickets sold. $\newline$ Cost of each single ticket: $\$31$ $\newline$ Number of single tickets sold: $x$ $\newline$ What is the total amount of money raised from single tickets? $\newline$ Cost of each single ticket $\times$ Number of single tickets sold $\newline$ $= 31 \times x$ $\newline$ $= 31x$ $\newline$ Total amount of money raised from single tickets: $31x$
Calculate Table Revenue: Determine the cost of reserving a table and the number of tables sold. $\newline$ Cost of reserving each table: $\$640$ $\newline$ Number of tables sold: $y$ $\newline$ What is the total amount of money raised from tables? $\newline$ Cost of reserving each table $\times$ Number of tables sold $\newline$ $= 640 \times y$ $\newline$ $= 640y$ $\newline$ Total amount of money raised from tables: $640y$
Combine Total Revenue: Combine the total amounts raised from single tickets and tables to form an expression for the total amount raised. $\newline$ Total amount raised from single tickets: $31x$ $\newline$ Total amount raised from tables: $640y$ $\newline$ What is the total amount raised from both single tickets and tables? $\newline$ Add total amount raised from single tickets and tables. $\newline$ $31x + 640y$
Set Fundraising Goal Inequality: Determine the inequality that represents the goal of raising more than $\$7,200$ . The candidate hopes to raise more than $\$7,200$ . The total amount raised must be greater than $\$7,200$ . Inequality: $31x + 640y > 7,200$

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