Section 3.5 Applications and Problem Solving 163 μ 5 Skill Practice 7. A piece of cable 92 ft long is to be cut into two pieces. One piece must be three times longer than the other. How long should each piece be? Answer 7. One piece should be 23 ft and the other should be 69 ft long. b. Let n represent the number of rides Alicia takes during the day. Rides cost $3 each. 3n is the total cost. c. Let D represent the amount of money that Annie made during the week. Josie made $430 less than Annie. D 430 represents the amount that Josie made. In Examples 5 and 6, we practice solving application problems using linear equations. Applying a Linear Equation to Carpentry A carpenter must cut a 10-ft board into two pieces to build a brace for a picnic table. If one piece needs to be four times longer than the other piece, how long should each piece be? Solution: We can let x represent the length of either piece. However, if we choose x to be the length of the shorter piece, then the longer piece has to be 4x (4 times as long). Let x the length of the shorter piece. Then 4x the length of the longer piece. Step 3: Write an equation in words. x 4x 10 Step 4: Write a mathematical equation. Step 5: Solve the equation. Combine like terms. Divide both sides by 5. Step 6: Interpret the results in words. x 4x 10 5x 10 5x 5 x 2 10 5 a Length of one piece b a length of the other piece b a total length b Example 5 Step 1: Read the problem completely. Step 2: Label the unknowns. Draw a picture. 10 ft x 4x Recall that x represents the length of the shorter piece. Therefore, the shorter piece is 2 ft. The longer piece is given by 4x or 412 ft2 8 ft. The pieces are 2 ft and 8 ft. Avoiding Mistakes In Example 5, the two pieces should total 10 ft.We have, 2 ft 8 ft 10 ft as desired.
miller_prealgebra_2e_ch1_3
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