Answer Key

Level 1

1. $13\text{ and }7$
2. $8\text{ dogs, }4\text{ cats}$
3. $10\text{ and }5$
4. $18\text{ girls, }12\text{ boys}$
5. $4\text{ pens, }6\text{ pencils}$
6. $12\text{ chickens, }8\text{ cows}$
7. $10\text{ cm by }5\text{ cm}$
8. $20\text{ and }5$

Answer Key

Level 2

1. $4\text{ adult, }4\text{ child}$
2. $5\text{ visits, }\$45$
3. $10\text{ dimes, }5\text{ quarters}$
4. $\text{coffee }\$3,\ \text{muffin }\$2$
5. $12\text{ two-point, }8\text{ five-point}$
6. $6\text{ miles, }\$15$
7. $14\text{ and }5$
8. $\text{apple }\$0.75,\ \text{banana }\$1$

Grade 8 Algebra: Word Problems: Systems of Equations

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Speed, mixtures, ages and digits

1. Solve:
$\text{A}$ $\text{boat}$ $\text{goes}$ $\text{24}$ $\text{miles}$ $\text{downstream}$ $\text{in}$ $\text{2}$ $\text{hours}$ $\text{and}$ $\text{back}$ $\text{upstream}$ $\text{in}$ $\text{3}$ $\text{hours.}$ $\text{Find}$ $\text{the}$ $\text{speed}$ $\text{of}$ $\text{the}$ $\text{boat}$ $\text{in}$ $\text{still}$ $\text{water}$ $\text{and}$ $\text{of}$ $\text{the}$ $\text{current.}$
2. Solve:
$\text{How}$ $\text{many}$ $\text{liters}$ $\text{of}$ $\text{a}$ $\text{20}$ $\text{percent}$ $\text{solution}$ $\text{and}$ $\text{a}$ $\text{40}$ $\text{percent}$ $\text{solution}$ $\text{make}$ $\text{10}$ $\text{liters}$ $\text{of}$ $\text{a}$ $\text{28}$ $\text{percent}$ $\text{solution?}$
3. Solve:
$\text{A}$ $\text{mother}$ $\text{is}$ $\text{3}$ $\text{times}$ $\text{as}$ $\text{old}$ $\text{as}$ $\text{her}$ $\text{son.}$ $\text{In}$ $\text{10}$ $\text{years}$ $\text{she}$ $\text{will}$ $\text{be}$ $\text{twice}$ $\text{as}$ $\text{old}$ $\text{as}$ $\text{him.}$ $\text{Find}$ $\text{their}$ $\text{ages}$ $\text{now.}$
4. Solve:
$\text{A}$ $\text{rectangle}$ $\text{has}$ $\text{a}$ $\text{perimeter}$ $\text{of}$ $\text{40}$ $m\text{.}$ $\text{Its}$ $\text{length}$ $\text{is}$ $\text{4}$ $m\text{}$ $\text{less}$ $\text{than}$ $\text{3}$ $\text{times}$ $\text{its}$ $\text{width.}$ $\text{Find}$ $\text{the}$ $\text{length}$ $\text{and}$ $\text{width.}$
5. Solve:
$\text{A}$ $\text{plane}$ $\text{flies}$ $\text{600}$ $\text{miles}$ $\text{with}$ $\text{the}$ $\text{wind}$ $\text{in}$ $\text{3}$ $\text{hours}$ $\text{and}$ $\text{600}$ $\text{miles}$ $\text{against}$ $\text{the}$ $\text{wind}$ $\text{in}$ $\text{4}$ $\text{hours.}$ $\text{Find}$ $\text{the}$ $\text{speed}$ $\text{of}$ $\text{the}$ $\text{plane}$ $\text{and}$ $\text{of}$ $\text{the}$ $\text{wind.}$
6. Solve:
$\text{A}$ $\text{concert}$ $\text{sold}$ $\text{500}$ $\text{tickets}$ $\text{for}$ $\text{9500}$ $\text{dollars.}$ $\text{Floor}$ $\text{seats}$ $\text{cost}$ $\text{25}$ $\text{dollars}$ $\text{and}$ $\text{balcony}$ $\text{seats}$ $\text{cost}$ $\text{15}$ $\text{dollars.}$ $\text{How}$ $\text{many}$ $\text{of}$ $\text{each}$ $\text{were}$ $\text{sold?}$
7. Solve:
$\text{One}$ $\text{phone}$ $\text{plan}$ $\text{costs}$ $\text{40}$ $\text{dollars}$ $\text{plus}$ $\text{0.10}$ $\text{dollars}$ $\text{per}$ $\text{text.}$ $\text{Another}$ $\text{costs}$ $\text{25}$ $\text{dollars}$ $\text{plus}$ $\text{0.25}$ $\text{dollars}$ $\text{per}$ $\text{text.}$ $\text{For}$ $\text{how}$ $\text{many}$ $\text{texts}$ $\text{are}$ $\text{they}$ $\text{equal,}$ $\text{and}$ $\text{what}$ $\text{is}$ $\text{the}$ $\text{cost?}$
8. Solve:
$\text{The}$ $\text{digits}$ $\text{of}$ $\text{a}$ $\text{two-digit}$ $\text{number}$ $\text{add}$ $\text{up}$ $\text{to}$ $\text{9.}$ $\text{Reversing}$ $\text{the}$ $\text{digits}$ $\text{makes}$ $\text{the}$ $\text{number}$ $\text{27}$ $\text{larger.}$ $\text{Find}$ $\text{the}$ $\text{number.}$

Answer Key

Level 3

1. $\text{boat }10\text{ mph, current }2\text{ mph}$
2. $6\text{ L of }20\%,\ 4\text{ L of }40\%$
3. $\text{son }10,\ \text{mother }30$
4. $14\text{ m by }6\text{ m}$
5. $\text{plane }175\text{ mph, wind }25\text{ mph}$
6. $200\text{ floor, }300\text{ balcony}$
7. $100\text{ texts, }\$50$
8. $36$