LINEAR EQUATIONS WORD PROBLEMS

Transcription

1 NAME PERIOD DATE LINEAR EQUATIONS WORD PROBLEMS 1. Bennett and his friends decide to go bowling. The cost for the group is $15 for shoe rentals plus $4.00 per game. a. Write an equation relating the total cost, C, of the outing to the number of games bowled, g. What is the independent variable? What is the dependent variable? b. How much will it cost them to bowl two games? Show your work. c. Graph the equation. Which variable should go on each axis? Choose sensible scales for the axes. d. Use the graph to estimate the number of games the group could bowl for $30.00

2 2. The Ace Telephone Co. charges a flat monthly fee of $22.00 for a telephone line and $0.20 per minute for long distance calls. a. Write an equation that will relate the total cost per month, C, to the number of minutes, m, of long distance calls you make. What form is your equation in? What is the dependent variable? What is the independent variable? b. If you make 25 minutes of long distance calls per month, what will it cost? Show your work. c. Sketch a graph of this equation for up To 100 minutes of calls. d. How many calls could you make if your phone budget is $30?

3 NAME DATE PERIOD LINEAR EQUATION WORD PROBLEMS Fill in the table with at least three ordered pairs including the initial value. Write an equation, graph, and solve for the given value. 1. Ms. Harris is tacking the progress of her plant s growth. Today the plant is 10 cm high. The plant grows 2.5 cm per day. a. Write a linear equation and model that represents the height of the plant after d days. b. What will the height of the plant be after 15 days? 2. Mrs. Johnson is on a diet. She currently weighs 200 pounds. He loses 5 pounds per month. a. Write a linear equation and model that represents Mrs. Johnson s weight after m months. b. After how many months will Mrs. Johnson reach her goal weight of 130 pounds?

4 3. Mr. Mason opens a savings account with $400. She saves $200 per month. Assume that he does not withdraw money or make any additional deposits. a. Write a linear equation and model that represents the total amount of money Mr. Mason deposits into his account after m months. b. After how many months will Ms. Lee have more than $2,000? 4. The population of Smyrna is 20,000 today. Every year the population of Smyrna increases by 500 people. a. Write a linear equation and model that represents the population of Smyrna x years from today. b. In approximately many years will the population of Smyrna exceed 40,000 people?

5 NAME DATE PERIOD SCATTER PLOTS AND THEIR CORRELATIONS Classify the scatter plots as having a positive, negative, or no correlation. 7. A history teacher asked her students how many hours of sleep they had the night before a test. The data below shows the number of hours the student slept and their score on the exam. Plot the data on a scatter plot and write a statement about the correlation.

6 Identify the data sets as having a positive, a negative, or no correlation. 8. The number of hours a person has driven and the number of miles driven 9. The number of siblings a student has and the grade they have in math class 10. The age of a car and the value of the car 11. The number of weeks a CD has been out and the total sales 12. The number of years a person went to school and their income 13. The number of songs downloaded on your cell phone and the amount of memory available 14. The amount of time spent on the computer instant messaging your friends and the number of computers in your house 15. The age of a house and the number of people living in the house Determine the correlation that exist in each graph

7 NAME DATE PERIOD LINE OF BEST FIT Make a scatter plot for each set of data. Eyeball the line of best fit and use a rule to draw it on your scatter plot. Then write the equation of the line of best fit. Use this equation to answer each question. 1. A student who waits on tables at a restaurant recorded the cost of meals and the tip left by single diners. 2. The table below gives the number of hours spent studying for a science exam (x) and the final exam grade (y).

8 3. The table below shows the lengths and corresponding ideal weights of sand sharks. 4. The table below gives the height and shoe sizes of six randomly selected men.

9 NAME DATE PERIOD Determine the line of best fit for each graph. DETERMINING LINE OF BEST FIT A small theme park is trying to determine the number of guests they should expect on a weekend, based on the temperature outside. Based on the trend line, about how many guests should be expected if the temperature is around 80?

10 Use the given line of best fit to approximate the rate of change relative to the scatter plot above.

11 Looking at the graph above showing a line of best fit, what is the correlation between the X and y variables?

12 Mrs. Moises, the school counselor, keeps a candy jar in her office for students. During one week, she kept count of how many students came to visit her and the number of candies in the jar, as shown in the scatter plot below. Based on the trend line, what is the best prediction for the number of candies in the jar when 30 students visit her? Predict the grade of a student if they studied for 3.5 hours.

13 NAME DATE PERIOD ANALYZING AND INTERPRETING GRAPHS Graph each person number of push-ups by 20 seconds increments. Use different color lines to represent each person. Be sure to properly label each axis and increment! Which person did the most push-ups? Who had the greatest rate of change in the first interval? The second? The final interval? Which person had the most consistent rate of change over the three intervals? Tell which graph corresponds to each situation below.

14 1. Gwendolyn started from home and walked to a friend s house. She stayed with her friend for a while and then walked to another friend s house farther from home. 2. Francisco started from home and walked to the store. After shopping, he walked back home. 3. Celia walks to the library at a steady pace without stopping. Pick the graph that BEST represents the situation s description. 4. A driver stopped her car for a traffic light. After waiting for the light to turn green, then the driver continued on her way. 5. A train pulls into a station lets off it s passengers. 6. A person parachutes from an airplane, free -falls for a while, open her chute, slows down, and lands on the ground.

15 NAME PERIOD DATE INTERPRETING GRAPHS The graphs give the speeds in mi/h of three people who are riding snowmobiles. Tell which graph corresponds to each situation. 1. David begins his ride slowly but then stops to talk with some friends. After a few minutes, he continues his ride, gradually increasing his speed. 2. Amber steadily increases her speed through most of her ride. Then she slows down as she nears some trees. 3. Kai steadily increases his speed for the first part of his ride. He then keeps a constant speed as he continues his ride. The graphs give the speeds in mi/h of three dogs during an obstacle course race. Tell which graph corresponds to each situation. 4. Brandy increases her speed throughout the race. 5. Bruno starts well but soon has to slow down to run around cones. After this, he steadily increases his speed. 6. Max gets off to a fast start and picks up speed. He slows down near the end of the race for a tunnel but then increases his speed right afterward. 7. Which graph most likely represents a car approaching a stop sign?

16 1. Which graph below could match the situation described? A car traveling at 0 mi/h accelerates to 25 mi/h over the first 5 seconds. It maintains that speed for the next 5 seconds, and then accelerates to 48 mi/h during the next 5 seconds. 2. Select a graph for the situation. You wait for the express bus for 30 minutes, get on and ride the bus nonstop for 3 miles, and then walk another mile to your home. 3. Which graph most likely describes the distance a person walks in a 24-hour period? Why?

17 NAME WINTER BREAK REVIEW Choose the correct table that matches the equation. Write the letter of the table on the line. PERIOD 1. y = -2x 2. y = x 5 3. y = -3x + 2 Match the correct equation with the table. Write the letter of the equation on the line. 4. x y x y

18 Match the table that correctly represents the line on the graph Match each table with the graph that represents the ordered pairs in the table. 8. x y A. B. C. 9. x y A. B. C.

19 Write the function rule for the following tables. Which equation correctly matches the graph?

20 18. Circle the scatterplot that most likely has a line of best fit represented by y = -2x + 1? 19. Based on the line of best fit, how much time does a teenager spend watching television if they spend 120 minutes on the computer?

21 Use a line of best fit to answer the following. 20. What type of correlation does this graph show? 21. Predict the distance travelled at time = Predict the distance travelled at time = 2 Use a line of best fit to answer the following. 23. What type of correlation does this graph show? 24. Predict the distance travelled at time = Predict the distance travelled at time = Draw the line of best fit. 27. What type of correlation does this graph show? 28. Calculate the slope of the line through points (10, 1970) and (20, 1980). 29. Write the equation of the line.

22 NAME DATE PERIOD EXAMPLE: TWO-WAY FREQUENCY TABLES 1. Among students who graduated, what is the proportion of boys? 2. Among students who are non-graduates, what proportion are girls? 1. Eighth grade students were asked whether they participate in an after-school activity. Complete the two-way frequency table below. Write 3 valid conclusions you can infer from the table Campbell students were polled about whether or not they owned an I-POD. The results of the Relative Percentage are shown below in percentage form. Complete the chart below. a. Did more students have I-Pods or not? *** C HALLE NGE * ** b. If there were a total of 88 students, how manywere 8th Graders?

23 3. You survey friends about the type of party they enjoy most. What type of party would you plan for them? Explain. Write a valid conclusion from the graph. 4. You go to a dance and help clean up afterwards. To help, you collect the soda cans, Coca-Cola and Sprite, and organize them. Some cans were on the table and some were in the garbage. Seventy-two total cans were found. 42 total cans were found in the garbage and fifty total cans were Coca-Cola. 14 Sprite cans were found on the table. Complete the two-way frequency chart. 5. Eighty students at Sagamore Middle school were surveyed whether they own an I-Pod. Half of the 50 eight graders said yes, and 28 of the seventh graders said yes. Complete the two-way frequency table. Make 3 valid conclusions about the data.

24 Exit Ticket Which is the most accurate line of best fit in the scatter plot below? A) b B) p C) g D) r Create a scatter plot from the data in the table below and describe the relationship shown. # of Days after planted Height of plant (in.) Create an equation that represents the line of best fit for the scatter plot below. y Height (in.) Equation (Show your work): x # Days

25 NAME DATE PERIOD INTERPRETING THE DATA 1. A survey of students in a homeroom class explored the relationship between gender and participation in the school band. Which is a reasonable conclusion to draw from these data? A) There are more band members in the class than non-band members. B) There are more boys in the class than girls. C) Among the boys, there are more boys in the band than Not in the band. D) More than one-half of the band members in the class are girls. 2. A survey of randomly selected Sagamore students explored the relationship between gender and video game play. Which is not a reasonable interpretation of the data? A) More boys surveyed play video game daily than girls. B) Ignoring gender, a little more than half of the students surveys play video games daily C) Of the boys surveyed, 5% do not play video games daily D) Of the girls surveyed, exactly 24% play video games daily 3. The following two-way table shows the number of students who voted for each of the two candidates for class president, by grade. How many more 8 th graders voted for Alessandro than Zoe? A) 15 B) 20 C) 40 D) The following two-way table shows the number of different color cars and SUV s at an auto dealership. What color is the least popular car in the dealership? A) White B) Red C) Green D) Blue 5. The two- way shows the results of a survey about whether students should be required to wear school uniforms. According to the table, what percent of teenagers are in favor of wearing school uniforms?

26 How many coaches participated in the survey? How many players participated in the survey? Which sport is more popular among the coaches? Which sport is more popular among the players?

27 NAME DATE PERIOD EXIT TICKET: TWO-WAY TABLES Directions: Create a two-table to display all data that is described and can be revealed. 1. It was found that 45 students own a laptop and 27 of these students do not own a four wheeler. There were 35 students that do not own a laptop and 12 of these students own a four wheeler. 2. It was found that 70 students own headphones and of these 22 students own an LED TVs. 70 students don't own headphones, but 45 of these students own an LED TV. 3. Students were having races in a pool and outside of the pool on the deck. It was found that 70 students were swimming and 22 of those students were racing. 70 students were not swimming and 45 of those students were racing on the deck. 4. The director had 205 dancers with mixed skills. 72 dancers were trained in both folk and classical dance. 43 trained in classical dance, but not folk. 62 dancers were not trained in either discipline.