# 6.5: Equations with Letters

**At Grade**Created by: CK-12

Look at the pictures of the scales below. Can you write equations to represent what you see on each scale? Can you figure out the value of each letter? In this concept, we will learn how to work with equations that represent what we see on scales. We will then learn how to solve sets of equations without scales.

### Guidance

In order to solve the problem above, we can write equations to represent what we see on each scale. We know that if we add the weights of each of the blocks on one scale together, the total weight must be the same as the number on the scale.

In order to figure out the values of the letters, go one letter at a time. First, figure out the value of x. Then, use that information to help find the value of y. Finally, once we know x and y figure out the value of z.

#### Example A

Write equations. Figure out the weights of the blocks.

**Solution:**

We can use the problem solving steps to help.

#### Example B

Write equations. Figure out the weights of the blocks.

**Solution:**

We can use the problem solving steps to help.

#### Example C

Eric wrote these equations from pictures of blocks on scales. Use Eric’s equations. Find the weight of each block.

**Solution:**

We can use the problem solving steps to help.

#### Concept Problem Revisited

We can use the problem solving steps to help.

### Vocabulary

In math, an ** unknown** is a letter that stands for a number that we do not yet know the value of. In this concept, the blocks that we did not know the weights of were

**. An**

*unknowns***is a math sentence that tells us two quantities that are equal. In this concept, we wrote**

*equation***with unknowns to represent what we saw on the scales. A**

*equations***is a set of equations that represents a given problem. Since we wrote multiple equations for each problem in this concept, we wrote a**

*system of equations***for each problem.**

*system of equations*### Guided Practice

1. Figure out the weight of each block:

2. Figure out the weight of each block:

3. Figure out the values of x, y, and z.

4. Figure out the values of x, y, and z.

**Answers:**

### Practice

Write equations. Figure out the weights of the blocks.

Figure out the values of x, y, and z.

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### Image Attributions

Students write equations to represent what they see on three scales. Then, they solve the equations. Finally, they solve systems of equations without first connecting them to scales. Students the problem solving steps to help.