# 5.5: Weight Problems

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

Look at the picture below. Can you figure out the weight of the green block? What about the yellow block? In this concept, we will learn how to find the weights of individual blocks given information about the weights of multiples or combinations of blocks.

### Guidance

In order to solve the problem above, use the problem solving steps.

- Start by
**describing**what information is given. - Then, identify what
**your job**is. In these problems, your job will be to figure out the weight of each individual block. - Next, make a
**plan**for how you will solve. In these problems, find the weight of the block using the scale that shows only one type of block first. - Then,
**solve**the problem. - Finally,
**check**your solution. Make sure that your solution causes each scale to have the correct weight.

#### Example A

Figure out the weight of each block.

**Solution:**

We can use the problem solving steps to help us.

\begin{align*}& \mathbf{Describe:} && \text{Two scales}\\ &&& E: \ \text{3 red blocks weigh 15 pounds}\\ &&& F: \ \text{1 red block and 1 green block weigh 14 pounds}\\ & \mathbf{My \ Job:} && \text{Figure out the weight of one red block and one green block.}\\ & \mathbf{Plan:} && \text{Start with} \ E. \ \text{Figure out the weight of one red block.}\\ &&& \text{In} \ F, \ \text{replace the red block with its weight.}\\ &&& \text{Figure out the weight of the green block.}\\ & \mathbf{Solve:} && E: \ \text{red block + red block + red block = 15 pounds, so one red block is 5 pounds.}\\ &&& F: \ \text{Replace red block with 5.}\\ &&& \text{Then 5 + green block = 14 pounds.}\\ &&& \text{Green block = 14 - 5, or 9 pounds.}\\ & \mathbf{Check:} && \text{Replace each red block with 5 pounds.}\\ &&& \text{Replace the green block with 9 pounds.}\\ &&& \text{Check with the scale weights.}\\ &&& E: \ \text{5+5+5=15 pounds} \quad F: \ \text{5+9=14 pounds}\end{align*}

#### Example B

Figure out the weight of each block.

**Solution:**

We can use the problem solving steps to help us.

\begin{align*}& \mathbf{Describe:} && \text{Two scales}\\ &&& G: \ \text{2 yellow blocks and 1 red block weigh 10 pounds}\\ &&& H: \ \text{2 red blocks weigh 12 pounds}\\ & \mathbf{My \ Job:} && \text{Figure out the weight of one red block and one yellow block.}\\ & \mathbf{Plan:} && \text{Start with} \ H. \ \text{Figure out the weight of one red block.}\\ &&& \text{In} \ G, \ \text{replace the red block with its weight.}\\ &&& \text{Figure out the weight of the yellow block.}\\ & \mathbf{Solve:} && H: \ \text{red block + red block =12 pounds, so one red block is 6 pounds.}\\ &&& G: \ \text{Replace red block with 6.}\\ &&& \text{Then 6 + yellow block +yellow block =10 pounds.}\\ &&& \text{ 2 yellow blocks = 10 - 6, or 4 pounds. Each yellow block is 2 pounds.}\\ & \mathbf{Check:} && \text{Replace each red block with 6 pounds.}\\ &&& \text{Replace each yellow block with 2 pounds.}\\ &&& \text{Check with the scale weights.}\\ &&& G: \ \text{2+2+6=10 pounds} \quad H: \ \text{6+6=12 pounds}\end{align*}

#### Example C

Figure out the weight of each block.

**Solution:**

We can use the problem solving steps to help us.

\begin{align*}& \mathbf{Describe:} && \text{Two scales}\\ &&& A: \ \text{3 blue blocks weigh 21 pounds}\\ &&& B: \ \text{1 blue block and 1 red block weigh 10 pounds}\\ & \mathbf{My \ Job:} && \text{Figure out the weight of one red block and one blue block.}\\ & \mathbf{Plan:} && \text{Start with} \ A. \ \text{Figure out the weight of one blue block.}\\ &&& \text{In} \ B, \ \text{replace the blue block with its weight.}\\ &&& \text{Figure out the weight of the red block.}\\ & \mathbf{Solve:} && A: \ \text{blue block + blue block + blue block = 21 pounds, so one blue block is 7 pounds.}\\ &&& B: \ \text{Replace blue block with 7.}\\ &&& \text{Then 7 + red block = 10 pounds.}\\ &&& \text{Red block = 10 - 7, or 3 pounds.}\\ & \mathbf{Check:} && \text{Replace each blue block with 7 pounds.}\\ &&& \text{Replace the red block with 3 pounds.}\\ &&& \text{Check with the scale weights.}\\ &&& A: \ \text{7+7+7=21 pounds} \quad B: \ \text{7+3=10 pounds}\end{align*}

#### Concept Problem Revisited

We can use the problem solving steps to help us.

\begin{align*}& \mathbf{Describe:} && \text{Two scales}\\ &&& C: \ \text{1 green block and 1 yellow block weigh 12 pounds}\\ &&& D: \ \text{2 green blocks weigh 16 pounds}\\ & \mathbf{My \ Job:} && \text{Figure out the weight of one green block and one yellow block.}\\ & \mathbf{Plan:} && \text{Start with} \ D. \ \text{Figure out the weight of one green block.}\\ &&& \text{In} \ C, \ \text{replace the green block with its weight.}\\ &&& \text{Figure out the weight of the yellow block.}\\ & \mathbf{Solve:} && D: \ \text{green block + green block = 16 pounds, so one green block is 8 pounds.}\\ &&& C: \ \text{Replace green block with 8.}\\ &&& \text{Then 8 + yellow block = 12 pounds.}\\ &&& \text{Yellow block = 12 - 8, or 4 pounds.}\\ & \mathbf{Check:} && \text{Replace each green block with 8 pounds.}\\ &&& \text{Replace the yellow block with 4 pounds.}\\ &&& \text{Check with the scale weights.}\\ &&& C: \ \text{8+4=12 pounds} \quad D: \ \text{8+8=16 pounds}\end{align*}

### 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, when you figured out the value of the individual blocks you were solving for

**.**

*unknowns*### Guided Practice

For each problem, figure out the weight of each block.

1.

2.

3.

**Answers:**

1. The green block is 3 pounds and the blue block is 4 pounds.

2. The red block is 7 pounds and the yellow block is 8 pounds.

3. The blue block is 10 pounds and the yellow block is 3 pounds.

### Practice

For each problem, figure out the weight of each block.

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### Image Attributions

In this concept, students determine the individual weights of two different blocks given information about the weights of multiples or combinations of blocks. Students use problem solving steps to help.