Section 2.4 Applications of Linear Equations: Introduction to Problem Solving 133 10 times the first integer ° ° ¢ 22 3 times the sum of the integers ¢ 10 times the first is 3 times integer 22 more than Step 4: Write a mathematical equation. Step 5: Solve the equation. Clear parentheses. Combine like terms. 10x 33 1x2 1x 12 1x 22 4 22 10x 31x x 1 x 22 22 10x 313x 32 22 10x 9x 9 22 10x 9x 31 10x 9x 9x 9x 31 x 31 The first integer is Step 6: Interpret the results and x 31. The second integer is write the x 1 31 1 32. The third integer is answer in words. x 2 31 2 33. The three integers are 31, 32, and 33. Skill Practice 5. Five times the smallest of three consecutive integers is 17 less than twice the sum of the integers. Find the integers. 4. Applications of Linear Equations Using a Linear Equation in an Application Example 6 A carpenter cuts a 6-ft board in two pieces. One piece must be three times as long as the other. Find the length of each piece. Solution: In this problem, one piece must be three times as long as the other. Thus, if x represents the length of one piece, then 3x can represent the length of the other. Step 1: Read the problem completely. x represents the length of the smaller piece. Step 2: Label the unknowns. 3x represents the length of the longer piece. Draw a figure. Answer 5. The integers are 11, 12, and 13. Step 3: Write a verbal model. Isolate the x-terms on one side. ⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩ the sum of the integers 3x x
miller_beginning_intermediate_algebra_4e_ch1_3
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