Algebraic Modeling Worksheet

Algebraic Modeling Practice

Read each problem carefully and follow the instructions to write algebraic expressions or equations. Show all your work.

1. Write an algebraic expression for "five less than twice a number x":  

2. Write an algebraic expression for "the sum of a number y and seven, divided by three":  

3. Write an algebraic expression for "the product of eight and a number z, increased by ten":  

1. A number increased by 15 is 37. Write an equation and solve for the number.

2. Three times a number, decreased by 9, is 21. Write an equation and solve for the number.

1. Which equation models the statement: "The perimeter of a rectangle is 48 cm. The length is 3 cm more than twice the width (w)."

1. The phrase "is less than" always translates to the subtraction symbol (-).

1. Sarah bought 3 notebooks and 2 pens. Each notebook costs $x and each pen costs $y. If she spent a total of $10, write an equation that represents this situation.

2. A taxi charges a flat fee of $2.50 plus $1.50 per mile (m). If a ride cost $13.00, write an equation to find the number of miles traveled.