Word Problem Solving with Equations: Examples and Solutions
Learn how to translate word phrases into algebraic expressions, solve word problems using equations, and apply problem-solving techniques with equations in one variable. Explore practical examples involving algebraic expressions, geometry, distances, and consecutive integers with detailed solutions provided.
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Presentation Transcript
1.8 & 1.9 WORDS INTO SYMBOLS PROBLEM SOLVING W/EQUATIONS translate word phrases into algebraic expressions and word sentences into equations solve word problems by using an equation in one variable
EXAMPLE 1: REPRESENT EACH WORD PHRASE AS AN ALGEBRAIC EXPRESSION a number decreased by 2 a. five more than three times a number b. twice the sum of a number and six c. the sum of twice a number and six d. the difference between a number and its square e.
EXAMPLE 2 The base of an isosceles triangle has length b cm and each base angle measures a . Find the measure of the vertex angle in terms of a. a. If the perimeter is 120 cm, find the length of one of the legs in terms of b. b.
EXAMPLE 3 A helicopter left Midcity airport at noon and flew east at 110 km/h. One hour later a light plane left Midcity flying west at 320 km/h. How far apart were the aircraft x hours after noon? Express your answer in terms of x. Rate (mi/h) Time (h) Distance (mi) helicopter plane
EXAMPLE 4 What is the sum of five consecutive odd integers if: The middle one is m? a. The next to largest is x? a.
EXAMPLE 5 At noon a cargo plane leaves McHare Airport and heads east at 180 mi/h. Its destination is Jamesville, 500 mi away. At 1:00 pm a jet takes off from McHare and flies east after the cargo plane at 450 mi/h. At what time will the jet overtake the cargo plane? Rate (mi/h) Time (h) Distance (mi) cargo plane jet
