This document provides examples for writing two-step equations to model word problems. It introduces the concept of using variables to represent unknown quantities and writing equations that translate the word problem into algebraic expressions. Several practice problems are provided where a variable is defined and an equation is written for each real-world situation described. Students are asked to solve some of the equations as homework.

1. Name ______________________________ Date ____________________
Mrs. Labuski / Mrs. Rooney Period _____ Writing Two-Step Equations
Many real-world situations can be modeled by two-step
equations. In order to find unknown quantities in these
situations, you must be able to translate words into equations.
EXAMPLES
Define a variable and write an equation for each situation.
A Seven less than three times a number is twenty.
Let n represent the number.
Seven less -7
three times a number  3n
is twenty  =20
3n – 7= 20
B Four more than a number divided by six is eleven.
Let y represent the number.
Four more  +4
a number divided by six y
6
is eleven =11
y+ 4 = 11
6

2. Define a variable and write an equation for each situation.
3. Two times a number plus 7. The product of six and some
eight is eighteen. number added to five is fifteen.
4. Twenty-four minus 5 times 8. Three plus 4 times a
a number is fifteen. number is twelve.
5. Two times a number minus 9. Six times a number minus
five is twelve. five is thirteen.
6. Six minus the product of 10. The product of some
four and some number is number and five is added to
fifteen. seven to give a total of
twenty-three.

3. Name __________________________________ Date ____________________
Mrs. Labuski / Mrs. Rooney Period __________ Writing Two-Step Equations HW
Write the algebraic equation, solve for the variable, and check.
1. Three times a number, increased by 1, is 25. Find the number.
2. If 3 is added to twice a number, the result is 17. Find the number.
3. 3 more than six times a number is 15. Find the number.
4. When a number is increased by 8, the result is 13. Find the number.

4. Name ______________________________ Date ____________________
Mrs. Labuski / Mrs. Rooney Period _____ Writing Two-Step Equations
Many real-world situations can be modeled by two-step
equations. In order to find unknown quantities in these
situations, you must be able to translate words into equations.
EXAMPLES
Define a variable and write an equation for each situation.
A Seven less than three times a number is twenty.
Let n represent the number.
Seven less -7
three times a number  3n
is twenty  =20
3n – 7= 20
B Four more than a number divided by six is eleven.
Let y represent the number.
Four more  +4
a number divided by six y
6
is eleven =11
y+ 4 = 11
6

5. Define a variable and write an equation for each situation.
3. Two times a number plus 7. The product of six and some
eight is eighteen. number added to five is fifteen.
2n + 8 = 18 5+6n=15
4. Twenty-four minus 5 times 8. Three plus 4 times a
a number is fifteen. number is twelve.
24-5n=15 3+4n=12
5. Two times a number minus 9. Six times a number minus
five is twelve. five is thirteen.
6n-5=13
2n-5=12
6. Six minus the product of 10. The product of some
four and some number is number and five is added to
fifteen. seven to give a total of
twenty-three.
7 + 5n = 23
6-4n=15