VIEWS: 120 PAGES: 13 POSTED ON: 7/2/2011
PROBLEM-SOLVING USING INEQUALITIES To solve word problems by using inequalities in one variable. Find all the sets of four consecutive even integers whose sum is between 225 and 250. 1. Define the variable: x = smallest consecutive even integer x + 2 = next consecutive even integer x + 4 = third consecutive even integer x + 6 = largest consecutive even integer Find all the sets all of four consecutive even integers whose sum is between 225 and 250. 2. Write an equation: 225 < x + (x + 2) + (x + 4) + (x + 6) < 250 Find all the sets all of four consecutive even integers whose sum is between 225 and 250. 3. Solve: 225 < x + (x + 2) + (x + 4) + (x + 6) < 250 225 < 4x + 12 < 250 225 < 4x + 12 and 4x + 12 < 250 213 < 4x 4x < 238 53.25 < x x < 59.5 Find all the sets all of four consecutive even integers whose sum is between 225 and 250. 53.25 < x and x < 59.5 X = 54 or 56 or 58 ANSWERS: 54, 56, 58, 60 56, 58, 60, 62 58, 60, 62, 64 A store is charged $5.50 each for calculators and a delivery charge of $25 for the order. If the store sells the calculators for $8 each, how many calculators must be ordered and sold to produce a profit of the $80? A store is charged $5.50 each for calculators and a delivery charge of $25 for the order. If the store sells the calculators for $8 each, how many calculators must be ordered and sold to produce a profit of at least $80? 1. Define the variable: c = calculators sold A store is charged $5.50 each for calculators and a delivery charge of $25 for the order. If the store sells the calculators for $8 each, how many calculators must be ordered and sold to produce a profit of at least $80? 2. Equation: 8c – (5.50c + 25) > 80 A store is charged $5.50 each for calculators and a delivery charge of $25 for the order. If the store sells the calculators for $8 each, how many calculators must be ordered and sold to produce a profit of at least $80? 3. Solve: 8c – 5.50c – 25 > 80 2.50c – 25 > 80 2.50c > 105 c > 42 at least 42 calculators 1. John's scores in his first four tests were 72, 74, 89, 91. What will he have to score on his next test to obtain a B- average? Define the Variable: x = fifth test score Write an inequality: 72 74 89 91 x 79.5 5 Solve: 326 x 79.5 5 326 x 397.5 x 71.5 John must score an 71.5% 2. The four sides of a square are increased by 10 cm, 20 cm, 30 cm and 40 cm respectively. The perimeter of the resulting quadrilateral is between five and six times the perimeter of the original square. What can you conclude about the length of the side of the original square? x + 40 Define the variable: x + 30 x + 10 x x + 20 Write an inequality: 16x < 100 and -20x < -100 x < 6.25 x>5 20x < 4x + 100 < 24x The original square had a length of Solve: between 5 and 6.25 cm. 20x < 4x + 100 and 4x + 100 < 24x 3. The cable company offers two types of service. With plan A, you can get basic cable per month for $42.50 and an additional $17.50 for all of the premium channels. With plan B, you can get basic cable for $42.50 with additional premium channels for a $1.25 per channel. How many premium channels which you need to order with plan B before plan A would become cheaper? Define the variable. Solve. c = number of 60 < 42.50 + 1.25c premium channels 17.50 < 1.25c ordered 14 < c Write an inequality. 42.50 + 17.50 < 42.50 + 1.25c You will need to order 15 additional premium channels for plan A to be cheaper. Pg. 71 2, 3, 4, 6, 7, 11