Writing Equations Worksheet

Writing Equations

Read each problem carefully and write an algebraic equation that represents the given situation. Define your variables clearly.

1. The sum of three consecutive even integers is 156. Write an equation to represent this situation. Let 'x' be the first even integer.

2. A rectangular garden has a perimeter of 80 feet. The length of the garden is 10 feet more than its width. Write an equation to represent the perimeter in terms of its width 'w'.

Translate the following verbal phrases into algebraic expressions or equations.

3. Five less than twice a number is equal to fifteen.  

4. The product of a number and seven, increased by ten, is forty-five.  

5. Which equation represents the statement: 'The square of a number decreased by 9 is 16'?

6. The equation for 'The sum of three consecutive integers is 21' can be written as x + x+1 + x+2 = 21.

Match the verbal phrase with its corresponding algebraic expression.

10. A car travels at a speed of 'v' miles per hour for 't' hours. If it covers a distance of 300 miles, write an equation relating speed, time, and distance.

11. The cost of producing 'x' items is given by a fixed cost of $500 plus $15 per item. If the total cost is $2000, write an equation to find the number of items produced.