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Analyzing One-Variable Inequalities in Context

Analyzing One-Variable Inequalities in Context 1.9 - Solution

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a
We are told that the drama class wants to raise at least $2500.\$2500. In an inequality, we would represent this by saying that the target sum has to be greater than or equal to $2500.\$2500. Target sum2500\begin{gathered} \text{Target sum}\geq 2500 \end{gathered} The target sum is the earnings from ticket sale and the donations of $470.\$470. Earnings from ticket sale+4702500\begin{gathered} \text{Earnings from ticket sale}+470\geq 2500 \end{gathered} If we let xx represent the number of tickets the drama class needs to sell, the product of xx and the price of a single ticket, $10,\$10, represents the earnings from ticket sale. 10x+4702500\begin{gathered} 10x+470 \geq 2500 \end{gathered} By solving the inequality for x,x, we can find the number of tickets they need to sell.
10x+470250010x+470 \geq 2500
10x203010x\geq2030
x203x\geq203
The drama class has to sell at least 203203 tickets to raise $2500.\$2500.
b

This inequality tells us that all values greater than or equal to 203203 will satisfy the inequality. Notice that xx can equal 203,203, which we show with a closed circle on the number line.