Grade 8 Algebra: Word Problems: Systems of Equations

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Sums, differences and simple totals

1. Solve:
$\text{The}$ $\text{sum}$ $\text{of}$ $\text{two}$ $\text{numbers}$ $\text{is}$ $\text{20}$ $\text{and}$ $\text{their}$ $\text{difference}$ $\text{is}$ $\text{6.}$ $\text{Find}$ $\text{the}$ $\text{numbers.}$
2. Solve:
$\text{A}$ $\text{shelter}$ $\text{has}$ $\text{12}$ $\text{cats}$ $\text{and}$ $\text{dogs.}$ $\text{There}$ $\text{are}$ $\text{4}$ $\text{more}$ $\text{dogs}$ $\text{than}$ $\text{cats.}$ $\text{How}$ $\text{many}$ $\text{of}$ $\text{each?}$
3. Solve:
$\text{The}$ $\text{sum}$ $\text{of}$ $\text{two}$ $\text{numbers}$ $\text{is}$ $\text{15.}$ $\text{One}$ $\text{number}$ $\text{is}$ $\text{twice}$ $\text{the}$ $\text{other.}$ $\text{Find}$ $\text{the}$ $\text{numbers.}$
4. Solve:
$\text{A}$ $\text{class}$ $\text{has}$ $\text{30}$ $\text{students.}$ $\text{There}$ $\text{are}$ $\text{6}$ $\text{more}$ $\text{girls}$ $\text{than}$ $\text{boys.}$ $\text{How}$ $\text{many}$ $\text{of}$ $\text{each?}$
5. Solve:
$\text{Pens}$ $\text{cost}$ $\text{2}$ $\text{dollars}$ $\text{and}$ $\text{pencils}$ $\text{cost}$ $\text{1}$ $\text{dollar.}$ $\text{Mia}$ $\text{buys}$ $\text{10}$ $\text{items}$ $\text{for}$ $\text{14}$ $\text{dollars.}$ $\text{How}$ $\text{many}$ $\text{pens}$ $\text{and}$ $\text{pencils?}$
6. Solve:
$\text{A}$ $\text{farm}$ $\text{has}$ $\text{chickens}$ $\text{and}$ $\text{cows}$ $\text{with}$ $\text{20}$ $\text{heads}$ $\text{and}$ $\text{56}$ $\text{legs}$ $\text{in}$ $\text{all.}$ $\text{How}$ $\text{many}$ $\text{of}$ $\text{each?}$
7. Solve:
$\text{A}$ $\text{rectangle}$ $\text{has}$ $\text{a}$ $\text{perimeter}$ $\text{of}$ $\text{30}$ $\text{cm.}$ $\text{Its}$ $\text{length}$ $\text{is}$ $\text{5}$ $\text{cm}$ $\text{more}$ $\text{than}$ $\text{its}$ $\text{width.}$ $\text{Find}$ $\text{the}$ $\text{length}$ $\text{and}$ $\text{width.}$
8. Solve:
$\text{The}$ $\text{sum}$ $\text{of}$ $\text{two}$ $\text{numbers}$ $\text{is}$ $\text{25.}$ $\text{The}$ $\text{larger}$ $\text{is}$ $\text{4}$ $\text{times}$ $\text{the}$ $\text{smaller.}$ $\text{Find}$ $\text{the}$ $\text{numbers.}$