Writing Two-Step Equations

Concept

Equations that can be solved in exactly two steps and gives the final value of the variable in two steps are called two step equations and are algebraic equations. Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers.

Rules

1. Define a variable.
2. Focus only on key words.
3. Translate the verbal model into an algebraic equation.

Example

Write an equation in terms of c.
Jayden purchased 3 CDs and 2 DVDs for $74. How much did each CD cost if each DVD was $17.50 and All 3 CDs were the same price?

Solution

1. Define a variable.
c represents the cost of one CD

2. Focus only on key words.
3 CDs plus 2 DVDs equals $74,
each DVD is $17.50

3. Translate the verbal model into an algebraic equation.
Equation: 3c + 2 (17.50) = 74.

Practice Writing Two-Step Equations

Practice Problem 1

Match the scenario with the appropriate expression in the answer set.
Raven went to the bakery to buy a small cake and several pastries. If the cake cost $5 and the pastries are $8 each, how much did Raven spend?

Practice Problem 2

Write an equation in terms of b, and solve it to answer the question. If necessary, round to the nearest hundredth.
Sanborn has a stamp collection. He found someone that has 12 of the stamps that he would like to add to his collection. If the total price of these stamps is $168, what is the price of each stamp?

Practice Problem 3

Write an equation in terms of y, and solve it to answer the question.
Chloe’s class is planning a field trip to the beach. Twenty-nine students want to participate in one of the two beach activities, and the rest want to fish from the dock. Two-thirds of the class plan to play games on the beach, and 7 students want to take a beach walk to look for sea stars and turtles. How many students want to fish on the dock?
Hint: First, find the number of students in Chloe’s class.