3b. Jamaal’s final grade in his math class is based upon a weighted average. The weights are as follows. Homework (10%) Quizzes (15%) Tests (50%) Final exam (25%) If Jamaal’s homework average is 85, quiz average is 80, and test average is 75, what does he need on his final exam to have at least a 70 average in the class? Solution 3b. What is unknown? The final exam grade is unknown. Let f represent the final exam grade. What is given? The final grade is calculated as follows. 10%(homework average) + 15%(quiz average) + 50%(test average) + 25%(final exam) = 0.10(85) + 0.15(80) + 0.50(75) + 0.25f To obtain the inequality, we use the following statement. Final grade is at least 70. 0.10(85) + 0.15(80) + 0.50(75) + 0.25f ≥ 70 8.5 + 12 + 37.5 + 0.25f ≥ 70 Multiply on the left. 58 + 0.25f ≥ 70 Combine like terms. 58 + 0.25f - 58 ≥ 70 - 58 Subtract 58 from each side. 0.25f ≥ 12 Simplify. 0.25f 12 ≥ 0.25 0.25 Divide each side by 0.25. f ≥ 48 Simplify. Jamaal needs at least a 48 on the final exam to have at least a 70 final grade. We can check by substituting a number greater than or equal to 48 into the original inequality to see that the final grade is at least 70. 3c. Susan uses a phone service provided by a high-speed Internet connection. The basic residential calling plan costs $14.99 for the first 500 min of local and long distance calling plus 3.9¢ for each additional minute. How many minutes can she use for her cost to be at most $20.00 per month? Solution 3c. What is unknown? The number of additional minutes over 500 is unknown. Let m represent the number of additional minutes. What is given? The monthly cost is represented by 14.99 + 0.039m. To obtain the inequality, we use the following statement. Monthly cost is at most 20. 14.99 + 0.039m ≤ 20 Translate to obtain the inequality. 14.99 + 0.039m - 14.99 ≤ 20 - 14.99 Subtract 14.99 from each side. 0.039m ≤ 5.01 Simplify. 0.039m 5.01 ≤ 0.039 0.039 Divide each side by 0.039. m ≤ 128.46 Simplify. Susan can talk for 128 additional minutes, or for a total of 628 min, for her cost to be at most $20. Translate the statement. 94 Chapter 2 Linear Equations and Inequalities in One Variable
hendricks_intermediate_algebra_1e_ch1_3
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