Answer Key

Level 1

1. $8:\ \$8\text{ per ticket}$
2. $12:\ \$12\text{ per hour}$
3. $50:\ 50\text{ mi per hour}$
4. $3:\ \$3\text{ per topping}$
5. $2:\ \text{grows 2 cm per week}$
6. $-4:\ \text{loses 4 L per min}$
7. $25:\ \text{saves \$25 per week}$
8. $-5:\ \text{drops 5\% per hour}$

Answer Key

Level 2

1. $\tfrac{1}{4}$
2. $\tfrac{2}{5}$
3. $\tfrac{1}{20}$
4. $-\tfrac{4}{5}$
5. $\$25\text{ per month}$
6. $-2\text{ cm per h}$
7. $-8\text{ ft per s}$
8. $\$15\text{ per h}$

Grade 8 Algebra: Word Problems: Slope and Rate of Change

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Using and comparing slopes

1. Solve:
$\text{A}$ $\text{safe}$ $\text{ramp}$ $\text{has}$ $\text{a}$ $\text{slope}$ $\text{of}$ $\text{at}$ $\text{most}$ $\text{1/12.}$ $\text{If}$ $\text{it}$ $\text{rises}$ $\text{2}$ $\text{ft,}$ $\text{what}$ $\text{is}$ $\text{the}$ $\text{shortest}$ $\text{run?}$
2. Solve:
$\text{A}$ $\text{pool}$ $\text{has}$ $\text{500}$ $\text{gallons}$ $\text{and}$ $\text{drains}$ $\text{at}$ $\text{25}$ $\text{gallons}$ $\text{per}$ $\text{minute.}$ $\text{How}$ $\text{much}$ $\text{is}$ $\text{left}$ $\text{after}$ $\text{8}$ $\text{minutes?}$
3. Solve:
$\text{A}$ $\text{hill}$ $\text{has}$ $\text{a}$ $\text{slope}$ $\text{of}$ $\text{0.15.}$ $\text{How}$ $\text{much}$ $\text{does}$ $\text{it}$ $\text{rise}$ $\text{over}$ $\text{a}$ $\text{run}$ $\text{of}$ $\text{200}$ $m\text{?}$
4. Solve:
$\text{Plan}$ $\text{1}$ $\text{costs}$ $\text{\$20}$ $\text{plus}$ $\text{\$5}$ $\text{per}$ $\text{month.}$ $\text{Plan}$ $\text{2}$ $\text{costs}$ $\text{\$10}$ $\text{per}$ $\text{month.}$ $\text{Which}$ $\text{cost}$ $\text{grows}$ $\text{faster?}$ $\text{After}$ $\text{how}$ $\text{many}$ $\text{months}$ $\text{are}$ $\text{they}$ $\text{equal?}$
5. Solve:
$\text{Snow}$ $\text{is}$ $\text{3}$ $\text{in}$ $\text{deep}$ $\text{at}$ $\text{2}$ $\text{pm}$ $\text{and}$ $\text{9}$ $\text{in}$ $\text{deep}$ $\text{at}$ $\text{5}$ $\text{pm.}$ $\text{At}$ $\text{this}$ $\text{rate,}$ $\text{how}$ $\text{deep}$ $\text{is}$ $\text{it}$ $\text{at}$ $\text{7}$ $\text{pm?}$
6. Solve:
$\text{A}$ $\text{car}$ $\text{is}$ $\text{worth}$ $\text{\$24000}$ $\text{new}$ $\text{and}$ $\text{\$18000}$ $\text{after}$ $\text{3}$ $\text{years.}$ $\text{Find}$ $\text{the}$ $\text{rate.}$ $\text{What}$ $\text{is}$ $\text{it}$ $\text{worth}$ $\text{after}$ $\text{5}$ $\text{years?}$
7. Solve:
$\text{The}$ $\text{top}$ $\text{of}$ $\text{a}$ $\text{ladder}$ $\text{is}$ $\text{12}$ $\text{ft}$ $\text{up}$ $\text{a}$ $\text{wall}$ $\text{and}$ $\text{its}$ $\text{base}$ $\text{is}$ $\text{5}$ $\text{ft}$ $\text{from}$ $\text{the}$ $\text{wall.}$ $\text{Find}$ $\text{the}$ $\text{slope}$ $\text{of}$ $\text{the}$ $\text{ladder.}$
8. Solve:
$\text{Ramp}$ $\text{1}$ $\text{rises}$ $\text{2}$ $\text{ft}$ $\text{over}$ $\text{10}$ $\text{ft.}$ $\text{Ramp}$ $\text{2}$ $\text{rises}$ $\text{3}$ $\text{ft}$ $\text{over}$ $\text{12}$ $\text{ft.}$ $\text{Which}$ $\text{is}$ $\text{steeper?}$

Answer Key

Level 3

1. $24\text{ ft}$
2. $300\text{ gal}$
3. $30\text{ m}$
4. $\text{Plan 2; 4 months}$
5. $13\text{ in}$
6. $-\$2000\text{ per year; } \$14000$
7. $\tfrac{12}{5}$
8. $\text{Ramp 2 } (\tfrac{1}{4}>\tfrac{1}{5})$