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# 6.4: Weighing Weights

Difficulty Level: At Grade Created by: CK-12

### 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 unknown 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 weights of the blocks.

Solution:

We can use the problem solving steps to help.

Describe: There are three scales, D, E, and F, with blocks. Scale D has a blue block and a 6 pound weight. Scale E has 3 red blocks. Scale F has one red block, one blue block, and one yellow block.

My Job: Figure out the weights of the blocks.

Plan: Start with D and find the weight of the blue block. Write the weight of the blue block on the pictures. Next, find the weight of the red block and write the weight of the red block on the pictures. Finally, find the weight of the yellow block.

Solve: Scale D tells us that blue block+6=9\begin{align*} \text{blue block} + 6 = 9\end{align*}, so the blue block is 3 pounds. Scale E tells us that 3 red blocks weigh 15 pounds, so each red block weighs 5 pounds. Finally, Scale F tells us that one red block, one blue block, and one yellow block together weigh 10 pounds. This means 3+5+yellow block =10\begin{align*}3+5+ \text{yellow block }=10\end{align*} so the yellow block weighs 2 pounds.

Check: Replace each block with its weight. Scale D: 6+3=9. Scale E: 5+5+5=15. Scale F: 3+5+2=10.

#### Example B

Figure out the weights of the blocks.

Solution:

We can use the problem solving steps to help.

Describe: There are three scales, G, H, and I, with blocks. Scale G has a yellow block and an 8 pound weight. Scale H has a red block and a yellow block. Scale I has 2 red blocks and one blue block.

My Job: Figure out the weights of the blocks.

Plan: Start with G and find the weight of the yellow block. Write the weight of the yellow block on the pictures. Next, find the weight of the red block using scale H and write the weight of the red block on the pictures. Finally, find the weight of the blue block using scale I.

Solve: Scale G tells us that yellow block+8=15\begin{align*} \text{yellow block} + 8 = 15\end{align*}, so the yellow block is 7 pounds. Scale H tells us that one yellow block and one red block weigh 10 pounds, so the red block must weigh 3 pounds. Finally, Scale I tells us that 2 red blocks and one blue block weigh 10 pounds. This means 3+3+blue block =10\begin{align*}3+3+ \text{blue block }=10\end{align*} so the blue block weighs 4 pounds.

Check: Replace each block with its weight. Scale G: 8+7=15. Scale H: 7+3=10. Scale I: 3+4+3=10.

#### Example C

Figure out the weights of the blocks.

Solution:

We can use the problem solving steps to help.

Describe: There are three scales, J, K, and L, with blocks. Scale J has a red block and a 10 pound block. Scale K has 2 red blocks and a blue block. Scale L has one red block, one blue block, and one yellow block.

My Job: Figure out the weights of the blocks.

Plan: Start with Scale J and find the weight of a red block. Write the weight of the red block on the pictures. Next, find the weight of the blue block using Scale K and write the weight of the blue block on the pictures. Finally, find the weight of the yellow block using Scale L.

Solve: Scale J tells us that red block+10=15\begin{align*} \text{red block} + 10 = 15\end{align*}, so the red block is 5 pounds. Scale K tells us that 2 red blocks and one blue block weigh 16 pounds, so 5+5+blue block=16\begin{align*}5+5+ \text{blue block}=16\end{align*} and the blue block must weigh 6 pounds. Finally, Scale L tells us that one red block, one blue block, and one yellow block together weigh 15 pounds. This means 6+5+yellow block =15\begin{align*}6+5+ \text{yellow block }=15\end{align*} so the yellow block weighs 4 pounds.

Check: Replace each block with its weight. Scale J: 10+5=15. Scale K: 6+5+5=16. Scale L: 6+5+4=15.

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

### Guided Practice

Figure out the weights of the blocks.

1.

2.

3.

1. The red block is 8 pounds, the yellow block is 6 pounds, and the blue block is 4 pounds.

2. The yellow block is 8 pounds, the blue block is 5 pounds, and the red block is 7 pounds.

3. The blue block is 7 pounds, the yellow block is 5 pounds, and the red block is 8 pounds.

### Practice

Figure out the weights of the blocks.

### Notes/Highlights Having trouble? Report an issue.

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Date Created:
Jan 18, 2013