The band teacher promises his class a pizza party if, during the fall fundraiser, they exceed the fundraising goal of $\$2,100$ . The students make $\$1$ for each candy bar sold and $\$4$ for each box of cookies. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of candy bars $\newline$ $y =$ the number of boxes of cookies $\newline$ Choices: $\newline$ (A) $4x + y < 2,100$ $\newline$ (B) $x + 4y < 2,100$ $\newline$ (C) $x + 4y > 2,100$ $\newline$ (D) $4x + y > 2,100$

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Write a linear inequality: word problems

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Q. The band teacher promises his class a pizza party if, during the fall fundraiser, they exceed the fundraising goal of

\$2,100

. The students make

\$1

for each candy bar sold and

\$4

for each box of cookies.

\newline

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

\newline

x =

the number of candy bars

\newline

y =

the number of boxes of cookies

\newline

Choices:

\newline

(A)

4x + y < 2,100

\newline

(B)

x + 4y < 2,100

\newline

(C)

x + 4y > 2,100

\newline

(D)

4x + y > 2,100

Define Variables: Define the variables based on the information given. $\newline$ The number of candy bars sold is represented by $x$ . $\newline$ The number of boxes of cookies sold is represented by $y$ . $\newline$ Each candy bar sold contributes $\$1$ to the fundraising total. $\newline$ Each box of cookies sold contributes $\$4$ to the fundraising total.
Determine Total Amount: Determine the total amount of money raised. $\newline$ The total amount of money raised from candy bars is $\$1$ times the number of candy bars, which is $1 \times x$ or simply $x$ . $\newline$ The total amount of money raised from boxes of cookies is $\$4$ times the number of boxes of cookies, which is $4 \times y$ . $\newline$ The total amount of money raised is the sum of the money from candy bars and cookies, which is $x + 4y$ .
Formulate Inequality: Formulate the inequality based on the fundraising goal. $\newline$ The fundraising goal is $\$2,100$ , and the band teacher promises a pizza party if this amount is exceeded. $\newline$ To exceed the goal, the total amount of money raised must be greater than $\$2,100$ . $\newline$ Therefore, the inequality that represents this situation is $x + 4y > 2,100$ .
Select Correct Inequality: Select the correct inequality from the given choices. $\newline$ The correct inequality that we have determined is $x + 4y > 2,100$ . $\newline$ Looking at the choices given: $\newline$ (A) $4x + y < 2,100$ (Incorrect, as it suggests the total is less than the goal and the coefficients are incorrect) $\newline$ (B) $x + 4y < 2,100$ (Incorrect, as it suggests the total is less than the goal) $\newline$ (C) $x + 4y > 2,100$ (Correct, as it suggests the total is greater than the goal) $\newline$ (D) $4x + y > 2,100$ (Incorrect, as the coefficients are incorrect) $\newline$ The correct choice is (C) $x + 4y > 2,100$ .