Section 2.2 The Addition Property of Equality 107 From the given information, we can write the equation. Four less has the eight than twice same result more than a number as a number. 2n - 4 = n + 8 2n - 4 - n = n + 8 - n Subtract n from each side. n - 4 =8 Simplify. n - 4 + 4 = 8 + 4 Add 4 to each side. n = 12 Simplify. Check: 2n - 4 = n + 8 Original equation 2(12) - 4 = 12 + 8 Replace n with 12. 24 - 4 = 20 Simplify each side. 20 = 20 Simplify. The solution, n = 12, checks in the original equation. So, the number that satisfies the given relationship is 12. 4b. The selling price of a new car is $24,891. The selling price is the base price plus fees and options. The base price is $22,985. What is the total of the fees and options? Solution 4b. What is unknown? The total fees and options are unknown. Let x represent the fees and options. What is known? • The selling price is the base price plus fees and options. • The selling price is $24,891. • The base price is $22,985. From the given information, we can write the equation. base price plus Selling price is fees and options. 24,891 = 22,985 + x 24,891 - 22,985 = 22,985 + x - 22,985 Subtract 22,985 from each side. 1906 = x Simplify. The total of the fees and options is $1906. We can check by replacing x with 1906. With application problems, we also want to check to make sure the answer is reasonable. It wouldn’t make sense to have a negative value for this answer nor would it make sense for the fees and options to be more than the selling price. Student Check 4 For each problem: (1) assign a variable to the unknown, (2) write an equation that represents the situation, (3) solve the equation, and (4) answer the question using complete sentences. a. Twice the sum of a number and 3 is the same as 4 less than the number. Find the number. b. The tuition for 15 credit hours for a new in-state student at Georgia Perimeter College, a community college in Atlanta, Georgia, is $1235 per semester for students entering in Fall 2012. Tuition plus mandatory fees is $1710 per semester. How much are the fees the student pays each semester? (Source: http://www.usg.edu/fiscal_affairs/documents/tuition_and_fees/FY2012_ Tuition_Rates.pdf)
hendricks_beginning_algebra_1e_ch1_3
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