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4.2: What's the Weight

Created by: CK-12

Look at the picture below. Can you figure out the weight of the blue block? Can you figure out the weight of the red 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.

$& \mathbf{Describe:} && \text{Two scales}\\&&& A: \ \text{1 blue block weighs 5 pounds}\\&&& B: \ \text{1 blue block and 1 green block weigh 6 pounds}\\& \mathbf{My \ Job:} && \text{Figure out the weight of one blue block and one green block.}\\& \mathbf{Plan:} && \text{Start with} \ A. \ \text{I already know that one blue block is 5 pounds.}\\&&& \text{In} \ B, \ \text{replace the blue block with its weight.}\\&&& \text{Figure out the weight of the green block.}\\& \mathbf{Solve:} && B: \ \text{Replace blue block with 5.}\\&&& \text{Then 5 + green block = 6 pounds.}\\&&& \text{Green block = 6 - 5, or 1 pound.}\\& \mathbf{Check:} && \text{Replace each blue block with 5 pounds.}\\&&& \text{Replace the green block with 1 pound.}\\&&& \text{Check with the scale weights.}\\&&& A: \ \text{5 = 5 pounds} \quad B: \ \text{5 + 1 = 6 pounds}$

Example B

Solution:

We can use the problem solving steps to help us.

$& \mathbf{Describe:} && \text{Two scales}\\&&& A: \ \text{1 red block and 1 green block weighs 10 pounds}\\&&& B: \ \text{1 green block weighs 8 pounds}\\& \mathbf{My \ Job:} && \text{Figure out the weight of one green block and one red block.}\\& \mathbf{Plan:} && \text{Start with} \ B. \ \text{I already know that one green block is 8 pounds.}\\&&& \text{In} \ A, \ \text{replace the green block with its weight.}\\&&& \text{Figure out the weight of the red block.}\\& \mathbf{Solve:} && A: \ \text{Replace green block with 8 pounds.}\\&&& \text{Then red block + 8 = 10 pounds.}\\&&& \text{Red block = 10 - 8, or 2 pounds.}\\& \mathbf{Check:} && \text{Replace each green block with 8 pounds.}\\&&& \text{Replace the red block with 2 pounds.}\\&&& \text{Check with the scale weights.}\\&&& A: \ \text{2 + 8 = 10 pounds} \quad B: \ \text{8 = 8 pounds}$

Example C

Figure out the weight of each block.

Solution:

We can use the problem solving steps to help us.

$& \mathbf{Describe:} && \text{Two scales}\\&&& A: \ \text{2 yellow blocks weigh 12 pounds}\\&&& B: \ \text{1 yellow block and 1 red block weigh 15 pounds}\\& \mathbf{My \ Job:} && \text{Figure out the weight of one yellow block and one red block.}\\& \mathbf{Plan:} && \text{Start with} \ A. \ \text{Figure out the weight of one yellow block.}\\&&& \text{In} \ B, \ \text{replace the yellow block with its weight.}\\&&& \text{Figure out the weight of the red block.}\\& \mathbf{Solve:} && A: \ \text{yellow block + yellow block = 12 pounds, so one yellow block is half of 12, or 6 pounds.}\\&&& B: \ \text{Replace yellow block with 6.}\\&&& \text{Then 6 + red block = 15 pounds.}\\&&& \text{Red block = 15 - 6, or 9 pounds.}\\& \mathbf{Check:} && \text{Replace each yellow block with 6 pounds.}\\&&& \text{Replace the red block with 9 pounds.}\\&&& \text{Check with the scale weights.}\\&&& A: \ \text{6 + 6 = 12 pounds} \quad B: \ \text{6 + 9 = 15 pounds}$

Concept Problem Revisited

We can use the problem solving steps to help us solve this problem.

$& \mathbf{Describe:} && \text{Two scales}\\&&& A: \ \text{2 blue blocks weigh 4 pounds}\\&&& B: \ \text{1 blue block and 1 red block weigh 6 pounds}\\& \mathbf{My \ Job:} && \text{Figure out the weight of one blue block and one red block.}\\& \mathbf{Plan:} && \text{Start with} \ A. \ \text{Figure out the weight of one blue block.}\\&&& \text{In} \ B, \ \text{replace the blue block with its weight.}\\&&& \text{Figure out the weight of the red block.}\\& \mathbf{Solve:} && A: \ \text{blue block + blue block = 4 pounds, so one blue block is half of 4, or 2 pounds.}\\&&& B: \ \text{Replace blue block with 2.}\\&&& \text{Then 2 + red block = 6 pounds.}\\&&& \text{red block = 6 - 2, or 4 pounds.}\\& \mathbf{Check:} && \text{Replace each blue block with 2 pounds.}\\&&& \text{Replace the red block with 4 pounds.}\\&&& \text{Check with the scale weights.}\\&&& A: \ \text{2 + 2 = 4 pounds} \quad B: \ \text{2 + 4 = 6 pounds}$

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.

1. Green block is 5 pounds; yellow block is 8 pounds.

2. Yellow block is 7 pounds; blue block is 2 pounds.

3. Red block is 6 pounds; green block is 1 pound.

Practice

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

Jan 18, 2013