Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
Use estimation to choose the best answer
Problem
A \(\$480\) backpack is \(17\%\) off. Use the \(10\%-\text{to}-20\%\) amount range to determine the most reasonable proposed discount from \(\$48\), \(\$82\), \(\$96\), and \(\$398\). Give a complete inequality with the proposed discount between the two bounds.
Big Picture
What this problem is really about
Since seventeen percent lies between ten percent and twenty percent, its discount on a positive price must lie between the corresponding dollar amounts. We’ll calculate those lower and upper bounds from the backpack price, then test which stated discount falls strictly inside the interval. The bounds give both a magnitude check and the complete inequality.
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