30. MODELING REAL LIFE The inequality \( 4 x+3 y \geq 90 \) represents the numbers \( x \) of multiple-choice questions and the numbers \( y \) of matching questions you can answ correctly to receive an A on a test. You answer 19 multiple-choice questions and 6 matching questions correctly. Do you receive an A on the test? Explain.
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To find out if you receive an A on the test, we can substitute the values \( x = 19 \) and \( y = 6 \) into the inequality \( 4x + 3y \geq 90 \). Calculating this gives \( 4(19) + 3(6) = 76 + 18 = 94 \). Since 94 is greater than 90, you indeed satisfy the inequality and, therefore, would receive an A on the test. This scenario is an excellent example of how inequalities can model real-life situations, such as educational performance criteria. Inequalities often help set benchmarks and thresholds, which can provide clarity on what is needed to succeed in various tasks or goals.
