23.5 Linear Equations and problem solving Objective: To apply equations to word problems and review for the quiz.
3Equation Strategy to Remember: When solving an equation, the goal is to get the variable by itself on one side of the equation.Addition and subtraction are inverse operations. (opposites)Multiplication and division are inverse operations. (opposites)
4Warm up ProblemA number is doubled and then increased by seven. The result is ninety-three. What is the original number??
5Warm up ProblemSix less than five times a number is the same as seven times the number. What is the number?
6Problem 1Brad is a waiter, and he gets paid $5.75 per hour, and he can keep his tips. He knows his tips average $8.80 per table.If he worked an eight-hour shift and took home $169.20, how many tables did he serve?
7Problem 2On May 18, 1990 the fastest speed of any national railroad was achieved by the French high speed train Train ´a Grande Vitess as it traveled over a distance from Cortalain to Tours, France.A commentator said that this speed was so fast that if it continued at that rate, the train would travel 6404 miles in 20 hours. How fast did the train travel on that date?
8Problem 3Two trains leave a train station at the same time. One train travels east at 50 mph. The other train travels west at 55mph.In how many hours will the two trains be 315 miles apart?
9TemperatureThe temperature in Fahrenheit is equivalent to nine-fifths the temperature in Celsius increased by 32.Write an equation for this relationship.A body temperature of 95°F or lower may indicate that a person has hypothermia. What temperature in the Celsius scale may indicate hypothermia?
10Problem 4In warmer climates, approximate temperature predictions can be made by counting the number of chirps a cricket makes during a minute. The temperature (in Fahrenheit) decreased by 40 is equivalent to one-forth of the number of cricket chirps in a minute.(a) Write an equation for this relationship.(b) Approximately how many chirps per minute should be recorded if the temperature is 90 F?(c) If a person recorded 48 cricket chirps in a minute, what would the temperature be?
11Problem 5 A page of your school yearbook is by 11 inches. The left margin is inch and the spaceto the right of the pictures is inches. Thespace between the pictures is inch. Howwide can the pictures be to fit three across thewidth of the page.
12Problem 6.At east high school, 579 students take Spanish. This number has been increasing at a rate of about 30 students per year. The number of students taking French is 217 and has been decreasing at a rate of about 2 students per year. At these rates, when will there be three times as many students taking Spanish as taking French
13Problem 7A gazelle can run 73 feet per second for several minutes. A cheetah can run 88 feet per second but can only sustain its top speed for about 20 seconds before it is worn out. How far away from the cheetah does the gazelle need to stay for it to be safe?
14Problem 8You are making flags for the school color guard. Each flag has a red stripe and a 12-inch wide white stripe. The width of each flag is ¾ its length. The length of the flag is inches. How wide is the red stripe?
15Problem 9Currently, you have $60 and your sister has $135. You decide to save $5 of your allowance each week, while your sister decides to spend her whole allowance plus $10 each week. How long will it be before you have as much money as your sister?