�� ������������������������ �������������������� Write an inequality that models each situation. Solve the inequality and answer the question in a complete sentence. 5a. Juanita has math test scores of 73, 85, and 80. What score does she need on her fourth math test to have a test average of at least 80? Solution 5a. What is unknown? The score on the fourth test is unknown. Let x represent the score on the fourth math test. What is known? The first three test scores are 73, 85, and 80. To obtain the inequality, we use the following statement. The average of the four test scores is at least 80. 73 + 85 + 80 + x 4 ≥ 80 238 + x 4 ≥ 80 4a238 + x 4 b ≥ 4(80) 238 + x ≥ 320 238 + x - 238 ≥ 320 - 238 x ≥ 82 Recall the average is the sum of all items the number of items Juanita needs at least an 82 on her fourth test to have at least an 80 test average. 5b. Jamaal’s final grade in his math class is based on a weighted average. The weights are as follows: Homework average 10% Quiz average 15% Test average 50% Final exam 25% If Jamaal’s homework average is 85, his quiz average is 80, and his test average is 75, what grade does he need on his final exam to have a final grade of at least 70 in the class? final grade of at least 80 in the class? Solution 5b. What is unknown? The final exam grade is unknown. Let x = final exam grade. + What is known? The final grade is calculated by 10% (home work average) + 15% (quiz average) + 50% (test average) + 25% (final exam) = 0.10 (home work average) + 0.15 (quiz average) + 0.50 (test average) + 0.25 (final exam) = 0.10(85) + 0.15(80) + 0.50(75) + 0.25x To obtain the inequalities, we use the following statements. Final grade is at least 70. Final grade is at least 80. 0.10(85) + 0.15(80) 0.10(85) + 0.15(80) + 0.50(75) + 0.25x ≥ 70 0.50(75) + 0.25x ≥ 80 8.5 + 12 + 37.5 + 0.25x ≥ 70 8.5+ 12 + 37.5 + 0.25x ≥ 80 58+ 0.25x ≥ 70 58+ 0.25x ≥ 80 58+ 0.25x - 58 ≥ 70 - 58 58+ 0.25x - 58 ≥ 80 - 58 0.25x ≥ 12 0.25x ≥ 22 0.25x 0.25 ≥ 12 0.25 0.25x 0.25 ≥ 22 0.25 x ≥ 48 x ≥ 88 Jamaal needs at least a 48 on the Jamaal needs at least an 88 on the final exam to have a grade of at final exam to have a grade of at least 70 in the class. least 80 in the class. . Simplify the numerator of the fraction. Multiply each side by 4. Simplify. Subtract 238 from each side. Simplify. 174 Chapter 2 Linear Equations and Inequalities in One Variable
hendricks_beginning_algebra_1e_ch1_3
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