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:
$\text{The}$ $\text{digits}$ $\text{of}$ $\text{a}$ $\text{two-digit}$ $\text{number}$ $\text{add}$ $\text{up}$ $\text{to}$ $\text{9.}$ $\text{Reversing}$ $\text{the}$ $\text{digits}$ $\text{makes}$ $\text{the}$ $\text{number}$ $\text{27}$ $\text{larger.}$ $\text{Find}$ $\text{the}$ $\text{number.}$