Section 1.3 The Order of Operations, Algebraic Expressions, and Equations 41 135. The difference of six times a number and 18 136. 6 less than four times the sum of a number and 1 137. Twice the product of a number and 15 138. The product of 18 and the sum of a number and 4 139. The product of 14 and a number increased by 9 140. The quotient of four times a number and 6 Write an algebraic expression that represents each unknown quantity. 141. Norma mixes a 5% salt solution with a 40% solution to get a 25% solution. Let x oz represent the volume of the 5% salt solution. If Norma wants 50 oz of 25% salt solution, write an expression that represents the volume of the 40% salt solution. 142. David mixes a 10% alcohol solution with a 50% solution to get a 20% solution. Let x mL be the volume of the 50% alcohol solution. If David wants to get 30 mL of 20% solution, write an expression that represents the volume of the 10% solution. 143. In a rectangle, the length is two more than three times the width. If w represents the width, write an expression that represents the length of the rectangle. 144. In a rectangle, the width is four less than twice the length. If l represents the length, write an expression that represents the width of the rectangle. Solve each problem. 145. The expression P(1 + r)t represents the amount of money in an account when P dollars is invested at an annual interest rate of r (in decimal form) for t yr. Find the amount of money that will be in an account at the end of 5 yr if $1500 is invested at 2% annual interest. (Hint: Convert 2% to a decimal value before substituting this value in the expression.) 146. The expression P(1 + r)t represents the amount of money in an account when P dollars is invested at an annual interest rate of r (in decimal form) for t yr. Find the amount of money that will be in an account at the end of 2 yr if $3200 is invested at 4% annual interest. (Hint: Convert 4% to a decimal value before substituting this value in the expression.) 147. The height of a baseball hit upward with an initial velocity of 120 ft/sec from an initial height of 6 ft is represented by the expression -16t2 + 120t + 6, where t is the number of seconds after the ball has been hit. What is the height of the ball after 5 sec? 148. The height of a baseball hit upward with an initial velocity of 95 ft/sec from an initial height of 4.5 ft is represented by the expression -16t2 + 95t + 4.5, where t is the number of seconds after the ball has been hit. What is the height of the ball after 4 sec? 149. At Central Pennsylvania Community College, in-state-resident tuition and fees for the academic year 2010–2011 were calculated by the expression 211c, where c is the number of credit units taken per semester. If Angela took 13 credits in Spring 2011, what was her tuition and fees? 150. At Los Angeles Valley College, in-state-resident tuition and fees for academic year 2010–2011 were calculated by the expression 26c + 42, where c is the number of units taken per semester. If Goran took 15 units in Spring 2011, what was his tuition and fees? You Be the Teacher! Correct each student’s errors, if any. 151. Evaluate the expression 3x2 - 2x + 1 for x = 2. Keith’s work: 3 · 22 - 2 · 2 + 1 = 62 - 4 + 1 = 36 - 4 + 1 = 33 152. Evaluate the expression - 2 3 x + 5 for x = 3. Frankie’s work: - 2 3 · 3 + 5=- 2 3 · 8=- 2 3 · 24 3 =- 48 9 153. Evaluate the expression 30 - 2x2 for x = 3. Lestine’s work: 30 - 2(3)2 = 28(32) = 28(9) = 252 154. Evaluate the expression u15 - 4xu for x = 3. Ian’s work: u15 - 4(3)u = u11(3)u = u33u = 33 155. Simplify the expression -3 · 22 + 28 ÷ 7 · 4 + 36. Basil’s work: -3 · 22 + 28 ÷ 7 · 4 + 36 = -62 + 28 ÷ 28 + 36 = -36 + 1 + 36 = 1 156. Simplify the expression 38 - 22 - 45 ÷ 5 · 3. Abul’s work: 38 - 22 - 45 ÷ 5 · 3 = 38 - 4 - 45 ÷ 15 = 38 - 4 - 3 = 31 Calculate It! Use a calculator to evaluate each algebraic expression. 157. x3 - 2x + 1 for x = 0, 2.5, and 3.2 158. 5x + 1 x - 1 for x = 1.5, 1.8, and 4 159. 1x2 - 9 for x = 3, 5, and 9 160. u500 - 3x2 u for x = 8.5, 10, and 12
hendricks_beginning_algebra_1e_ch1_3
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