## Key Concepts

- Write and solve an addition equation.
- Write and solve a subtraction equation.
- Solve problems using equations.

**Introduction: **

**Solving an equation:**

You can solve an equation by using a bar diagram, a balance, or an equation.

You can also use inverse relationship and the properties of equality to solve equations.

**4.3.1 Write and solve an addition equation**

**Example 1:**

Joan had some markers. After she bought 12 more markers, she had 16. How many markers did Joan have at the start? Let *n* represent the number of markers Joan had at the start.

**Solution:**

**One way:**

You can find the value of *n* by getting it alone on one side of the equation.

**Another way:**

Draw a bar diagram to represent the situation.

*n* + 12 = 16

**Solve the addition equation. **

*n* + 12 = 16

*n* + 12 – 12 = 16 – 12

* n =* 4

To check, substitute 4 for *n*.

*n* + 12 = 16

4 + 12 = 16

* *16 = 16

**4.3.2 Write and solve a subtraction equation**

**Example 2:**

Judy is 9 years younger than Grace. Judy is 12. Write and solve a subtraction equation to find Grace’s age, *x*.

**Solution:**

Draw a bar diagram to represent the situation.

*x* – 9 = 12

*x* – 9 + 9 = 12 + 9

*x* = 21

Substitute 21 for *y* to check your work.

*x* – 9 = 12

21 – 9 = 12

21 = 12

**4.3.3 Solve problems using equations**

**Example 3:**

Louis read 14 fewer pages than he was assigned to read. He read 60 pages. Write and solve an equation to find how many pages, *p*, Louis was assigned to read.

**Solution:**

Draw a bar diagram to represent the situation.

**One way:**

Write and solve an addition equation.

*p* + 14 = 60

*p* + 14 – 14 = 60 – 14

* p =* 46

**Another way:**

Write and solve a subtraction equation.

*p* = 60 – 14

*p* = 46

**Example 4:**

A group of students were on a school bus. At the last stop, the bus picked up 16 students, and the bus arrived at school with 25 students. How many students were on the bus before the last stop?

**Solution:**

Draw a bar diagram to represent the situation.

**One way:**

Write and solve an addition equation.

*n* + 16 = 25

*n* + 16 – 16 = 25 – 16

* n =* 9

**Another way:**

Write and solve a subtraction equation.

*n* = 25 – 16

*n* = 9

# Exercise:

- Solve the following equation.

g – 8 = 25 - Solve the following equation.

25 + y =42 - Explain how to get the variable alone from the following equation.
*x*+ 13 = 25*x*+ 13 – 13 = 25 – ? - Explain how to get the variable alone from the following equation.
*n*– 30 = 10*x*– 30 + 30 = 10 + ? - The Olympic triathlon is about 51 km. A contestant has completed two of the three legs of the race and has traveled 42 km. Solve 42 +
*d*= 51 to find the distance of the third leg. - Jo loaned Al $15. She had $15 left. Solve the equation 15 = s – 15 to find how much money Jo had before she made the loan.
- Explain how to solve the equation 35 + p = 92. Then solve.
- Explain how you can use the inverse relationship of addition and subtraction to solve the equation n + 7 = 25.
- You have some baseball trading cards. You give 21 baseball cards to a friend and have 9 left for yourself. How many baseball cards were in your original deck? Write and solve an equation to find t, the number of baseball cards in your original deck.

10. What operation should be used to solve the equation 153 = g + 45? Solve the equation.

### What have we learned:

- Write and solve an addition equation by using a bar diagram, a balance, or an equation.
- Write and solve a subtraction equation by using a bar diagram, a balance, or an equation.
- Solve problems using addition or subtraction equations.