Question

# Your goal is to sell at least 50 boxes of cookies for your school fundraiser. a. Write an inequality that represents your goal. b. You sell 26 boxes. Write and solve a new inequality to represent how many boxes you need to sell to reach your goal.

Solution

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$\textbf{Given:}$

Need to sell at least $50$ boxes of cookies for fundraiser.

let the number of boxes to be sold is given by $x$.

(a.)

Inequality is $x\geq50$.

(b.)

$26$ boxes are sold.

Let $y$ represent the remaining number of boxes.

$\Rightarrow y=x-26$.

$\therefore x=26+y$

Put the value of $x$ in inequality we got in part (a).

$\Rightarrow 26+y\geq50$

Subtract $26$ from both side of inequality:

$26+y-26\geq50-26$

$\Rightarrow y\geq24$.

So for reaching goal $24$ boxes are still remaining to sell.

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