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Alana is selling handmade jewelry to earn money for camp. Bracelets sell for $\$5$ and necklaces sell for $\$30$ , and she needs to make at least $\$620$ in revenue to cover the cost of camp. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of bracelets $\newline$ $y =$ the number of necklaces $\newline$ Choices: $\newline$ (A) $30x + 5y \geq 620$ $\newline$ (B) $30x \times 5y \geq 620$ $\newline$ (C) $5x - 30y \geq 620$ $\newline$ (D) $5x + 30y \geq 620$

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Write two-variable inequalities: word problems

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Q. Alana is selling handmade jewelry to earn money for camp. Bracelets sell for

\$5

and necklaces sell for

\$30

, and she needs to make at least

\$620

in revenue to cover the cost of camp.

\newline

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

\newline

x =

the number of bracelets

\newline

y =

the number of necklaces

\newline

Choices:

\newline

(A)

30x + 5y \geq 620

\newline

(B)

30x \times 5y \geq 620

\newline

(C)

5x - 30y \geq 620

\newline

(D)

5x + 30y \geq 620

Calculate Revenue per Item: Determine the revenue per item. Alana sells bracelets for $\$5$ each and necklaces for $\$30$ each. Therefore, the revenue from selling $x$ bracelets is $5x$ dollars and the revenue from selling $y$ necklaces is $30y$ dollars.
Form Combined Revenue Inequality: Combine the revenues to form an inequality. Alana needs to make at least $\$620$ , so the combined revenue from bracelets and necklaces must be greater than or equal to $\$620$ . The inequality that represents this situation is $5x$ (bracelets revenue) plus $30y$ (necklaces revenue) must be at least $\$620$ .
Write Inequality in Standard Form: Write the inequality in standard form. The standard form of an inequality is $Ax + By \geq C$ , where $A$ and $B$ are coefficients and $C$ is a constant. In this case, $A$ is the revenue per bracelet, $B$ is the revenue per necklace, and $C$ is the total revenue needed. Therefore, the inequality is $5x + 30y \geq 620$ .

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