Grade 8 Algebra: Word Problems: Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Comparisons and averages

1. Write an inequality and solve:
$\text{Plan}$ $\text{1}$ $\text{costs}$ $\text{25}$ $\text{dollars}$ $\text{plus}$ $\text{3}$ $\text{dollars}$ $\text{per}$ $\text{visit.}$ $\text{Plan}$ $\text{2}$ $\text{costs}$ $\text{7}$ $\text{dollars}$ $\text{per}$ $\text{visit.}$ $\text{For}$ $\text{how}$ $\text{many}$ $\text{visits}$ $v\text{}$ $\text{is}$ $\text{Plan}$ $\text{1}$ $\text{cheaper?}$
2. Write an inequality and solve:
$\text{A}$ $\text{rectangle}$ $\text{has}$ $\text{width}$ $w\text{}$ $\text{and}$ $\text{its}$ $\text{length}$ $\text{is}$ $\text{twice}$ $\text{the}$ $\text{width.}$ $\text{Its}$ $\text{perimeter}$ $\text{is}$ $\text{at}$ $\text{most}$ $\text{36}$ $\text{cm.}$ $\text{Find}$ $\text{the}$ $\text{possible}$ $\text{widths.}$
3. Write an inequality and solve:
$\text{Leo}$ $\text{earns}$ $\text{8}$ $\text{dollars}$ $\text{per}$ $\text{hour}$ $\text{plus}$ $\text{a}$ $\text{20}$ $\text{dollar}$ $\text{bonus.}$ $\text{He}$ $\text{wants}$ $\text{more}$ $\text{than}$ $\text{100}$ $\text{dollars.}$ $\text{How}$ $\text{many}$ $\text{hours}$ $h\text{?}$
4. Write an inequality and solve:
$\text{The}$ $\text{sum}$ $\text{of}$ $\text{three}$ $\text{consecutive}$ $\text{integers}$ $\text{is}$ $\text{less}$ $\text{than}$ $\text{60.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{largest}$ $\text{possible}$ $\text{smallest}$ $\text{integer}$ $n\text{?}$
5. Write an inequality and solve:
$\text{Test}$ $\text{scores}$ $\text{are}$ $\text{82}$ $\text{and}$ $\text{90.}$ $\text{The}$ $\text{average}$ $\text{of}$ $\text{three}$ $\text{tests}$ $\text{must}$ $\text{be}$ $\text{at}$ $\text{least}$ $\text{85.}$ $\text{What}$ $\text{third}$ $\text{score}$ $s\text{}$ $\text{is}$ $\text{needed?}$
6. Write an inequality and solve:
$\text{Mia}$ $\text{has}$ $\text{200}$ $\text{dollars}$ $\text{and}$ $\text{spends}$ $\text{15}$ $\text{dollars}$ $\text{per}$ $\text{week.}$ $\text{Tom}$ $\text{has}$ $\text{80}$ $\text{dollars}$ $\text{and}$ $\text{saves}$ $\text{10}$ $\text{dollars}$ $\text{per}$ $\text{week.}$ $\text{After}$ $\text{how}$ $\text{many}$ $\text{weeks}$ $w\text{}$ $\text{does}$ $\text{Tom}$ $\text{have}$ $\text{more?}$

Answer Key

Level 3

1. $25 + 3v < 7v,\; v > 6.25 \;(\text{7 or more})$
2. $6w \le 36,\; w \le 6$
3. $8h + 20 > 100,\; h > 10$
4. $3n + 3 < 60,\; n < 19 \;(n = 18)$
5. $\dfrac{82 + 90 + s}{3} \ge 85,\; s \ge 83$
6. $80 + 10w > 200 - 15w,\; w > 4.8 \;(\text{5 weeks})$