Grade 8 Algebra: Word Problems: Linear Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Writing equations

1. Solve:
$\text{A}$ $\text{gym}$ $\text{charges}$ $\text{a}$ $\text{20}$ $\text{dollar}$ $\text{sign-up}$ $\text{fee}$ $\text{plus}$ $\text{15}$ $\text{dollars}$ $\text{per}$ $\text{month.}$ $\text{Write}$ $\text{an}$ $\text{equation}$ $\text{for}$ $\text{the}$ $\text{total}$ $\text{cost}$ $y\text{}$ $\text{after}$ $x\text{}$ $\text{months.}$
2. Solve:
$\text{A}$ $\text{plant}$ $\text{is}$ $\text{4}$ $\text{cm}$ $\text{tall}$ $\text{and}$ $\text{grows}$ $\text{2}$ $\text{cm}$ $\text{per}$ $\text{week.}$ $\text{Write}$ $\text{an}$ $\text{equation}$ $\text{for}$ $\text{its}$ $\text{height}$ $y\text{}$ $\text{after}$ $x\text{}$ $\text{weeks.}$
3. Solve:
$\text{A}$ $\text{taxi}$ $\text{charges}$ $\text{3}$ $\text{dollars}$ $\text{plus}$ $\text{2}$ $\text{dollars}$ $\text{per}$ $\text{mile.}$ $\text{Write}$ $\text{an}$ $\text{equation}$ $\text{for}$ $\text{the}$ $\text{cost}$ $y\text{}$ $\text{of}$ $\text{a}$ $\text{ride}$ $\text{of}$ $x\text{}$ $\text{miles.}$
4. Solve:
$\text{Sam}$ $\text{has}$ $\text{50}$ $\text{dollars}$ $\text{and}$ $\text{spends}$ $\text{5}$ $\text{dollars}$ $\text{each}$ $\text{day.}$ $\text{Write}$ $\text{an}$ $\text{equation}$ $\text{for}$ $\text{the}$ $\text{money}$ $y\text{}$ $\text{left}$ $\text{after}$ $x\text{}$ $\text{days.}$
5. Solve:
$\text{A}$ $\text{pool}$ $\text{holds}$ $\text{200}$ $\text{gallons}$ $\text{and}$ $\text{is}$ $\text{filled}$ $\text{at}$ $\text{25}$ $\text{gallons}$ $\text{per}$ $\text{minute}$ $\text{starting}$ $\text{from}$ $\text{empty.}$ $\text{Write}$ $\text{an}$ $\text{equation}$ $\text{for}$ $\text{the}$ $\text{water}$ $y\text{}$ $\text{after}$ $x\text{}$ $\text{minutes.}$
6. Solve:
$\text{A}$ $\text{phone}$ $\text{plan}$ $\text{costs}$ $\text{30}$ $\text{dollars}$ $\text{per}$ $\text{month}$ $\text{plus}$ $\text{10}$ $\text{dollars}$ $\text{per}$ $\text{GB}$ $\text{of}$ $\text{data.}$ $\text{Write}$ $\text{an}$ $\text{equation}$ $\text{for}$ $\text{the}$ $\text{monthly}$ $\text{cost}$ $y\text{}$ $\text{for}$ $x\text{}$ $\text{GB.}$
7. Solve:
$\text{A}$ $\text{candle}$ $\text{is}$ $\text{12}$ $\text{in}$ $\text{tall}$ $\text{and}$ $\text{burns}$ $\text{1}$ $\text{in}$ $\text{per}$ $\text{hour.}$ $\text{Write}$ $\text{an}$ $\text{equation}$ $\text{for}$ $\text{its}$ $\text{height}$ $y\text{}$ $\text{after}$ $x\text{}$ $\text{hours.}$
8. Solve:
$\text{A}$ $\text{worker}$ $\text{earns}$ $\text{18}$ $\text{dollars}$ $\text{per}$ $\text{hour}$ $\text{plus}$ $\text{a}$ $\text{40}$ $\text{dollar}$ $\text{bonus.}$ $\text{Write}$ $\text{an}$ $\text{equation}$ $\text{for}$ $\text{the}$ $\text{pay}$ $y\text{}$ $\text{for}$ $x\text{}$ $\text{hours.}$

Answer Key

Level 1

1. $y = 15x + 20$
2. $y = 2x + 4$
3. $y = 2x + 3$
4. $y = -5x + 50$
5. $y = 25x$
6. $y = 10x + 30$
7. $y = -x + 12$
8. $y = 18x + 40$

Grade 8 Algebra: Word Problems: Linear Functions

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Finding the equation from two facts

1. Solve:
$\text{A}$ $\text{rental}$ $\text{costs}$ $\text{70}$ $\text{dollars}$ $\text{for}$ $\text{2}$ $\text{days}$ $\text{and}$ $\text{130}$ $\text{dollars}$ $\text{for}$ $\text{5}$ $\text{days.}$ $\text{Write}$ $\text{an}$ $\text{equation}$ $\text{for}$ $\text{the}$ $\text{cost}$ $y\text{}$ $\text{for}$ $x\text{}$ $\text{days.}$
2. Solve:
$\text{A}$ $\text{plant}$ $\text{was}$ $\text{9}$ $\text{cm}$ $\text{tall}$ $\text{after}$ $\text{2}$ $\text{weeks}$ $\text{and}$ $\text{15}$ $\text{cm}$ $\text{tall}$ $\text{after}$ $\text{5}$ $\text{weeks.}$ $\text{Write}$ $\text{an}$ $\text{equation}$ $\text{for}$ $\text{its}$ $\text{height,}$ $\text{and}$ $\text{give}$ $\text{its}$ $\text{starting}$ $\text{height.}$
3. Solve:
$\text{A}$ $\text{phone}$ $\text{battery}$ $\text{shows}$ $\text{90}$ $\text{percent}$ $\text{after}$ $\text{1}$ $\text{hour}$ $\text{and}$ $\text{60}$ $\text{percent}$ $\text{after}$ $\text{4}$ $\text{hours.}$ $\text{Write}$ $\text{an}$ $\text{equation}$ $\text{for}$ $\text{the}$ $\text{battery}$ $y\text{}$ $\text{after}$ $x\text{}$ $\text{hours.}$
4. Solve:
$\text{A}$ $\text{caterer}$ $\text{charges}$ $\text{230}$ $\text{dollars}$ $\text{for}$ $\text{10}$ $\text{guests}$ $\text{and}$ $\text{390}$ $\text{dollars}$ $\text{for}$ $\text{18}$ $\text{guests.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{cost}$ $\text{per}$ $\text{guest}$ $\text{and}$ $\text{the}$ $\text{fixed}$ $\text{fee?}$
5. Solve:
$\text{Plan}$ $\text{1}$ $\text{costs}$ $\text{25}$ $\text{dollars}$ $\text{plus}$ $\text{5}$ $\text{dollars}$ $\text{per}$ $\text{class.}$ $\text{Plan}$ $\text{2}$ $\text{costs}$ $\text{10}$ $\text{dollars}$ $\text{per}$ $\text{class.}$ $\text{After}$ $\text{how}$ $\text{many}$ $\text{classes}$ $\text{do}$ $\text{they}$ $\text{cost}$ $\text{the}$ $\text{same?}$
6. Solve:
$\text{A}$ $\text{hiker}$ $\text{is}$ $\text{2}$ $\text{miles}$ $\text{from}$ $\text{camp}$ $\text{after}$ $\text{1}$ $\text{hour}$ $\text{and}$ $\text{8}$ $\text{miles}$ $\text{from}$ $\text{camp}$ $\text{after}$ $\text{4}$ $\text{hours,}$ $\text{walking}$ $\text{away}$ $\text{at}$ $\text{a}$ $\text{steady}$ $\text{pace.}$ $\text{How}$ $\text{far}$ $\text{will}$ $\text{the}$ $\text{hiker}$ $\text{be}$ $\text{after}$ $\text{6}$ $\text{hours?}$
7. Solve:
$\text{Water}$ $\text{in}$ $\text{a}$ $\text{tank}$ $\text{is}$ $\text{140}$ $\text{liters}$ $\text{after}$ $\text{3}$ $\text{minutes}$ $\text{and}$ $\text{100}$ $\text{liters}$ $\text{after}$ $\text{5}$ $\text{minutes}$ $\text{of}$ $\text{draining.}$ $\text{How}$ $\text{much}$ $\text{water}$ $\text{was}$ $\text{there}$ $\text{at}$ $\text{the}$ $\text{start?}$
8. Solve:
$\text{A}$ $\text{store}$ $\text{charges}$ $\text{4}$ $\text{dollars}$ $\text{per}$ $\text{notebook.}$ $\text{Another}$ $\text{charges}$ $\text{2.5}$ $\text{dollars}$ $\text{per}$ $\text{notebook}$ $\text{plus}$ $\text{a}$ $\text{6}$ $\text{dollar}$ $\text{fee.}$ $\text{For}$ $\text{how}$ $\text{many}$ $\text{notebooks}$ $\text{are}$ $\text{the}$ $\text{costs}$ $\text{equal?}$

Answer Key

Level 3

1. $y = 20x + 30$
2. $y = 2x + 5,\ 5\text{ cm}$
3. $y = -10x + 100$
4. $\$20\text{ per guest},\ \$30\text{ fee}$
5. $5\text{ classes}$
6. $12\text{ miles}$
7. $200\text{ liters}$
8. $4\text{ notebooks}$

Word Problems: Linear Functions: Classroom Packet

Grade 8 Algebra: Word Problems: Linear Functions

Level 1

Answer Key

Level 1

Grade 8 Algebra: Word Problems: Linear Functions

Level 2

Answer Key

Level 2

Grade 8 Algebra: Word Problems: Linear Functions

Level 3

Answer Key

Level 3