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4.3: What's the Weight

Difficulty Level: At Grade Created by: CK-12

What’s the Weight? – Solve for Unknowns

Teacher Notes

Given two scales, each holding one, two, or three blocks of two different types, students have to figure out the weights of the individual blocks. They do this by first identifying the scale that holds only one type of block (one unknown) and solving for the weight of that block. Next, students replace that block with its weight on the other scale, and then solve for the weight of the second block.

These problems provide introduction to the solution of systems of two equations with two unknowns. Each scale represents one equation, and can be represented symbolically. For example, a scale that shows two cubes with a total weight of 4 pounds can be displayed as \begin{align*}x + x = 4\end{align*}x+x=4.

Solutions

What’s the Weight? 1

  1. Cube is 5 pounds; sphere is 1 pound
  2. Sphere is 8 pounds; cylinder is 2 pounds

What’s the Weight? 2

  1. Triangular prism is 6 pounds; cylinder is 9 pounds
  2. Sphere is 5 pounds; triangular prism is 8 pounds

What’s the Weight? 3

  1. Triangular prism is 7 pounds; cube is 2 pounds
  2. Cylinder is 6 pounds; sphere is 1 pound

What’s the Weight? 4

  1. Cube is 5 pounds; sphere is 3 pounds
  2. Cylinder is 7 pounds; triangular prism is 2 pounds

What’s the Weight?

(Teacher page)

\begin{align*}& \mathbf{Describe:} && \text{Two scales}\\ &&& A: \ \text{2 cubes weigh 40 pounds}\\ &&& B: \ \text{1 cube and 1 cylinder weigh 6 pounds}\\ & \mathbf{My \ Job:} && \text{Figure out the weight of one cube and one cylinder.}\\ & \mathbf{Plan:} && \text{Start with} \ A. \ \text{Figure out the weight of one cube.}\\ &&& \text{In} \ B, \ \text{replace the cube with its weight.}\\ &&& \text{Figure out the weight of the cylinder.}\\ & \mathbf{Solve:} && A: \ \text{cube + cube = 4 pounds, so one cube is half of 4, or 2 pounds.}\\ &&& B: \ \text{Replace cube with 2.}\\ &&& \text{Then 2 + cylinder = 6 pounds.}\\ &&& \text{Cylinder = 6 - 2, or 4 pounds.}\\ & \mathbf{Check:} && \text{Replace each cube with 2 pounds.}\\ &&& \text{Replace the cylinder with 4 pounds.}\\ &&& \text{Check with the scale weights.}\\ &&& A: \ \text{2 + 2 = 4 pounds} \quad B: \ \text{2 + 4 = 6 pounds}\end{align*}

What’s the Weight? 1

Figure out the weight of each block.

What’s the Weight? 2

Figure out the weight of each block.

What’s the Weight? 3

Figure out the weight of each block.

What’s the Weight? 4

Figure out the weight of each block.

Extra for Experts: What’s the Weight? – Solve for Unknowns

Solutions

Extra for Experts: What’s the Weight? 1

  1. Cylinder is 3 pounds; sphere is 9 pounds
  2. Cube is 1 pound; cylinder is 8 pounds

Extra for Experts: What’s the Weight? 2

  1. Triangular prism is 2 pounds; sphere is 6 pounds
  2. Cube is 3 pounds; triangular prism is 7 pounds

Extra for Experts: What’s the Weight? 1

Extra for Experts: What’s the Weight? 2

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CK.MAT.ENG.SE.1.Algebra-Explorations-K-7.4.3