# Math Essay

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Tatiyana Young November 8, 2014 18596333 Module 2 Algebraic Equations and Inequalities Exercise 2.1 Math Problems 1. If 5 times the value of a number is increased by 3, the result is 28. What is the number? 5x+3=28 5x=25 X=5 2. If 4 times the reciprocal of a number is 3 more than 5/2 times the reciprocal of that number, find the number. 4×1/3=3+(5/2)×(1/x) 4/x=3+5/2x 4/x=(6x+5)/2 8=6x+5 6x=3 X=1/2 3. John had \$30,000 to invest. He invested part of this money in bonds paying 12% annual simple interest and the rest of the money in a savings account giving 4% annual interest. At the end of the year, he received \$2,400 as extra income. How much money did John place in each investment? .4x+.12(30000-x)=2400 .04x+.12(30000)-.12x=2400 .04x+3600-.12x=2400 .12x-.04x+3600=2400 .08x+3600=2400 .08x+3600-3600=2400-3600 8x=1200 (8x/8)=1200/8 X=1500 15000-30000=15000 Total invested at .12=\$15,000.00 At .04=\$15,000.00 15000*.04=\$600.00 15000*.12=\$1,800.00 \$1,800.00+\$600.00=\$2,400.00 4. The length of a football field is 180 feet more than its width. If the perimeter of the field is 1,060 feet, find the length of the field. L = W + 180 2L + 2W = 1060 substitute: 2(W + 180) + 2W = 1060 2W + 360 + 2W = 1060 4W = 700 W = 175ft L = 175 + 180 = 355ft check: 2(355) + 2(175) = 1060 710 + 350 = 1060 checks The field is 355 feet long. 5. At a school choir concert, 256 students are standing in rows. If the number of students in each row is equal to the total number of rows, find the number of students in each row. = = 16 So, the total number of students in each row is 16 6. If 6 times a number is decreased by 8, the result is 40. What is the number? 6x - 8 = 40 6x = 48 x = 8 7. Merry had \$20,000