Grade 8 Algebra: Word Problems: Solving Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Geometry, ages and comparisons

1. Write an equation and solve:
$\text{A}$ $\text{garden}$ $\text{is}$ $\text{3}$ $\text{meters}$ $\text{longer}$ $\text{than}$ $\text{it}$ $\text{is}$ $\text{wide.}$ $\text{Its}$ $\text{perimeter}$ $\text{is}$ $\text{34}$ $\text{meters.}$ $\text{Find}$ $\text{the}$ $\text{width}$ $w\text{.}$
2. Write an equation and solve:
$\text{Gym}$ $\text{A}$ $\text{costs}$ $\text{30}$ $\text{dollars}$ $\text{plus}$ $\text{5}$ $\text{dollars}$ $\text{per}$ $\text{visit.}$ $\text{Gym}$ $B\text{}$ $\text{costs}$ $\text{8}$ $\text{dollars}$ $\text{per}$ $\text{visit.}$ $\text{After}$ $\text{how}$ $\text{many}$ $\text{visits}$ $v\text{}$ $\text{do}$ $\text{they}$ $\text{cost}$ $\text{the}$ $\text{same?}$
3. Write an equation and solve:
$\text{Leo}$ $\text{is}$ $\text{4}$ $\text{years}$ $\text{older}$ $\text{than}$ $\text{Sara.}$ $\text{Their}$ $\text{ages}$ $\text{add}$ $\text{up}$ $\text{to}$ $\text{30.}$ $\text{How}$ $\text{old}$ $\text{is}$ $\text{Sara?}$ $\text{Use}$ $s\text{}$ $\text{for}$ $\text{her}$ $\text{age.}$
4. Write an equation and solve:
$\text{The}$ $\text{sum}$ $\text{of}$ $\text{three}$ $\text{consecutive}$ $\text{integers}$ $\text{is}$ $\text{72.}$ $\text{Find}$ $\text{the}$ $\text{smallest}$ $\text{integer}$ $n\text{.}$
5. Write an equation and solve:
$\text{A}$ $\text{shirt}$ $\text{costs}$ $\text{20}$ $\text{dollars}$ $\text{on}$ $\text{sale.}$ $\text{That}$ $\text{is}$ $\text{5}$ $\text{dollars}$ $\text{less}$ $\text{than}$ $\text{half}$ $\text{the}$ $\text{original}$ $\text{price}$ $p\text{.}$ $\text{Find}$ $p\text{.}$
6. Write an equation and solve:
$\text{Plan}$ $\text{A}$ $\text{costs}$ $\text{40}$ $\text{dollars}$ $\text{plus}$ $\text{2}$ $\text{dollars}$ $\text{per}$ $\text{GB.}$ $\text{Plan}$ $B\text{}$ $\text{costs}$ $\text{25}$ $\text{dollars}$ $\text{plus}$ $\text{5}$ $\text{dollars}$ $\text{per}$ $\text{GB.}$ $\text{For}$ $\text{how}$ $\text{many}$ $\text{GB}$ $g\text{}$ $\text{do}$ $\text{they}$ $\text{cost}$ $\text{the}$ $\text{same?}$

Answer Key

Level 3

1. $2(w + 3) + 2w = 34,\; w = 7$
2. $30 + 5v = 8v,\; v = 10$
3. $s + (s + 4) = 30,\; s = 13$
4. $3n + 3 = 72,\; n = 23$
5. $\tfrac{1}{2}p - 5 = 20,\; p = 50$
6. $40 + 2g = 25 + 5g,\; g = 5$