Practice
Solving Word Problems Using Linear Models Practice
Fifty original questions covering contextual rates, starting values, models, tables, predictions, comparisons, and multi-step interpretation.
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Question 1
Explanation
The coefficient of the independent variable is the rate. Here it is the heat index rises \(0.5\) unit per hour. The sign gives direction and the units come from output per input.
Question 2
Explanation
The coefficient of the independent variable is the rate. Here it is the stored mass falls by \(50\) kilograms per day. The sign gives direction and the units come from output per input.
Question 3
Explanation
The coefficient of the independent variable is the rate. Here it is the total increases by \(\$75\) per week. The sign gives direction and the units come from output per input.
Question 4
Explanation
The coefficient of the independent variable is the rate. Here it is the hiker gains \(100\) feet per hour. The sign gives direction and the units come from output per input.
Question 5
Explanation
The coefficient of the independent variable is the rate. Here it is the temperature falls \(2.5\) degrees celsius per minute. The sign gives direction and the units come from output per input.
Question 6
Explanation
The constant term is the dependent variable's value when the input equals zero. Therefore, it represents the fixed charge before labor.
Question 7
Explanation
The constant term is the dependent variable's value when the input equals zero. Therefore, it represents the starting balance in dollars.
Question 8
Explanation
The constant term is the dependent variable's value when the input equals zero. Therefore, it represents the value when purchased.
Question 9
Explanation
The constant term is the dependent variable's value when the input equals zero. Therefore, it represents the starting distance from the station.
Question 10
Explanation
The constant term is the dependent variable's value when the input equals zero. Therefore, it represents there are 75 seedlings at day zero.
Question 11
Explanation
Define the input as day and the output as crates. Compute \((200-120)/(5-1)=20\). The rate is \(20\) crates per day.
Question 12
Explanation
Define the input as minute and the output as elevation (m). Compute \((620-740)/(6-2)=-30\). The rate is \(-30\) meters per minute.
Question 13
Explanation
Define the input as week and the output as balance ($). Compute \((410-260)/(8-3)=30\). The rate is \(30\) dollars per week.
Question 14
Explanation
Define the input as hour and the output as temperature (°c). Compute \((6-18)/(5-1)=-3\). The rate is \(-3\) degrees Celsius per hour.
Question 15
Explanation
Define the input as day and the output as visitors. Compute \((700-450)/(7-2)=50\). The rate is \(50\) visitors per day.
Question 16
Explanation
Define the independent variable named in the prompt and the modeled output. The starting value is the constant term, while the per-unit change is the coefficient. This gives \(V=900-35d\).
Question 17
Explanation
Define the independent variable named in the prompt and the modeled output. The starting value is the constant term, while the per-unit change is the coefficient. This gives \(C=24+8.5m\).
Question 18
Explanation
Define the independent variable named in the prompt and the modeled output. The starting value is the constant term, while the per-unit change is the coefficient. This gives \(H=12+2.4w\).
Question 19
Explanation
Define the independent variable named in the prompt and the modeled output. The starting value is the constant term, while the per-unit change is the coefficient. This gives \(T=18-1.5h\).
Question 20
Explanation
Define the independent variable named in the prompt and the modeled output. The starting value is the constant term, while the per-unit change is the coefficient. This gives \(B=320+45w\).
Question 21
Explanation
The model defines the output in terms of elapsed input. Substitute the stated input: \(450-18(12)=234\). The result is the requested modeled quantity.
Question 22
Explanation
The model defines the output in terms of elapsed input. Substitute the stated input: \(72+9(8)=144\). The result is the requested modeled quantity.
Question 23
Explanation
The model defines the output in terms of elapsed input. Substitute the stated input: \(1{,}200+65(6)=1{,}590\). The result is the requested modeled quantity.
Question 24
Explanation
The model defines the output in terms of elapsed input. Substitute the stated input: \(30-2.5(7)=12.5\). The result is the requested modeled quantity.
Question 25
Explanation
The model defines the output in terms of elapsed input. Substitute the stated input: \(5+0.8(15)=17\). The result is the requested modeled quantity.
Question 26
Explanation
Set the modeled output equal to the requested target. Solving \(420=120+30w\), so \(300=30w\) and \(w=10\). The variable represents the requested elapsed input.
Question 27
Explanation
Set the modeled output equal to the requested target. Solving \(280=680-40h\), so \(-400=-40h\) and \(h=10\). The variable represents the requested elapsed input.
Question 28
Explanation
Set the modeled output equal to the requested target. Solving \(42=14+3.5d\), so \(28=3.5d\) and \(d=8\). The variable represents the requested elapsed input.
Question 29
Explanation
Set the modeled output equal to the requested target. Solving \(199=55+12m\), so \(144=12m\) and \(m=12\). The variable represents the requested elapsed input.
Question 30
Explanation
Set the modeled output equal to the requested target. Solving \(1{,}350=900+75t\), so \(450=75t\) and \(t=6\). The variable represents the requested elapsed input.
Question 31
Explanation
The output at input zero supplies the intercept. Dividing an output change by its corresponding input change supplies the constant slope. Both features agree with \(T=8h+30\).
Question 32
Explanation
The output at input zero supplies the intercept. Dividing an output change by its corresponding input change supplies the constant slope. Both features agree with \(W=240-12d\).
Question 33
Explanation
The output at input zero supplies the intercept. Dividing an output change by its corresponding input change supplies the constant slope. Both features agree with \(M=480+15t\).
Question 34
Explanation
The output at input zero supplies the intercept. Dividing an output change by its corresponding input change supplies the constant slope. Both features agree with \(T=12-2m\).
Question 35
Explanation
The output at input zero supplies the intercept. Dividing an output change by its corresponding input change supplies the constant slope. Both features agree with \(C=18-0.15p\).
Question 36
Explanation
Use the known observation as an anchor rather than assuming it is the intercept. Five years pass, so add \(5(20)=100\) to \(250\). The requested value is \(350\).
Question 37
Explanation
Use the known observation as an anchor rather than assuming it is the intercept. Move three minutes backward, so add back \(3(40)=120\) to \(900\). The requested value is \(1020\).
Question 38
Explanation
Use the known observation as an anchor rather than assuming it is the intercept. Seven days pass, so \(180+7(25)=355\). The requested value is \(355\).
Question 39
Explanation
Use the known observation as an anchor rather than assuming it is the intercept. Move five months backward: \(740-5(60)=440\). The requested value is \(440\).
Question 40
Explanation
Use the known observation as an anchor rather than assuming it is the intercept. Four minutes pass: \(34-4(2.5)=24\). The requested value is \(24\).
Question 41
Explanation
Define the shared input from the prompt and set the two outputs equal. \(40+6x=70+3x\), so \(3x=30\), giving the common-input value \(10\).
Question 42
Explanation
Define the shared input from the prompt and set the two outputs equal. \(120+8n=200+4n\), so \(4n=80\), giving the common-input value \(20\).
Question 43
Explanation
Define the shared input from the prompt and set the two outputs equal. \(25+12h=85+7h\), so \(5h=60\), giving the common-input value \(12\).
Question 44
Explanation
Define the shared input from the prompt and set the two outputs equal. \(300-15d=180-5d\), so \(120=10d\), giving the common-input value \(12\).
Question 45
Explanation
Define the shared input from the prompt and set the two outputs equal. \(50+2.5w=20+4w\), so \(30=1.5w\), giving the common-input value \(20\).
Question 46
Explanation
Define the model input with the units stated in the problem. Convert \(0.75\) hour to \(45\) minutes, then compute \(900-12(45)=360\). The contextual answer is \(360\).
Question 47
Explanation
Define the model input with the units stated in the problem. Use the linear growth first: \(250+45(10)=700\), then subtract the one-time fee. The contextual answer is \(620\).
Question 48
Explanation
Define the model input with the units stated in the problem. The rate is \((1600-1240)/(9-3)=60\); move back three years: \(1240-3(60)=1060\). The contextual answer is \(1060\).
Question 49
Explanation
Define the model input with the units stated in the problem. The yearly rate is \((510-760)/(7-2)=-50\); three more years gives \(510-3(50)=360\). The contextual answer is \(360\).
Question 50
Explanation
Define the model input with the units stated in the problem. Solve \(11+1.7m<6+2.2m\), obtaining \(m>10\); the least whole mile is \(11\). The contextual answer is \(11\).
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Questions to review
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- Question 1Interpreting contextual slopeEasy
- Question 2Interpreting contextual slopeEasy
- Question 3Interpreting contextual slopeEasy
- Question 4Interpreting contextual slopeEasy
- Question 5Interpreting contextual slopeEasy
- Question 6Interpreting initial valueEasy
- Question 7Interpreting initial valueEasy
- Question 8Interpreting initial valueEasy
- Question 9Interpreting initial valueEasy
- Question 10Interpreting initial valueEasy
- Question 11Finding rate from dataEasy
- Question 12Finding rate from dataEasy
- Question 13Finding rate from dataEasy
- Question 14Finding rate from dataEasy
- Question 15Finding rate from dataEasy
- Question 16Building a linear modelMedium
- Question 17Building a linear modelMedium
- Question 18Building a linear modelMedium
- Question 19Building a linear modelMedium
- Question 20Building a linear modelMedium
- Question 21Evaluating a contextual modelMedium
- Question 22Evaluating a contextual modelMedium
- Question 23Evaluating a contextual modelMedium
- Question 24Evaluating a contextual modelMedium
- Question 25Evaluating a contextual modelMedium
- Question 26Solving a linear model for inputMedium
- Question 27Solving a linear model for inputMedium
- Question 28Solving a linear model for inputMedium
- Question 29Solving a linear model for inputMedium
- Question 30Solving a linear model for inputMedium
- Question 31Building a model from a tableMedium
- Question 32Building a model from a tableMedium
- Question 33Building a model from a tableMedium
- Question 34Building a model from a tableMedium
- Question 35Building a model from a tableMedium
- Question 36Predicting from a nonzero observationMedium
- Question 37Predicting from a nonzero observationMedium
- Question 38Predicting from a nonzero observationMedium
- Question 39Predicting from a nonzero observationMedium
- Question 40Predicting from a nonzero observationMedium
- Question 41Comparing linear modelsHard
- Question 42Comparing linear modelsHard
- Question 43Comparing linear modelsHard
- Question 44Comparing linear modelsHard
- Question 45Comparing linear modelsHard
- Question 46Multi-step linear modelingHard
- Question 47Multi-step linear modelingHard
- Question 48Multi-step linear modelingHard
- Question 49Multi-step linear modelingHard
- Question 50Multi-step linear modelingHard