Math Problem Statement
Solve the puzzle involving the four equations: □ + □ = 4, □ + □ = 2, □ - □ = 5, □ = 7
Solution
Let's break down the math puzzle in the image and solve it step by step.
The puzzle consists of 4 equations involving boxes that we need to solve for:
- □ + □ = 4
- □ + □ = 2
- □ - □ = 5
- □ = 7
We'll solve this systematically by substituting and solving the unknowns.
From equation (4):
- □ = 7 (this gives us one of the boxes as 7)
Now let's substitute the value 7 into the remaining equations.
For equation (3):
- □ - 7 = 5
- Solving for the other box:
- □ = 5 + 7 = 12
- So, the second box is 12.
Now, let's use these values in equation (2):
- 7 + □ = 2
- Solving for the missing box:
- □ = 2 - 7 = -5
- So, another box is -5.
Finally, for equation (1):
- 12 + □ = 4
- Solving for the last box:
- □ = 4 - 12 = -8
- So, the last box is -8.
Summary of the solution:
- The four values are: 7, 12, -5, and -8.
Would you like further explanation on any of the steps or calculations?
Here are 5 follow-up questions to consider:
- What is the method used to solve a system of equations?
- How can substitution help solve for multiple variables?
- What happens when negative numbers are introduced into equations?
- How can we verify if all values satisfy the given puzzle?
- What are some other methods to solve puzzles with multiple unknowns?
Tip: Always double-check your solution by substituting values back into the original equations!
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Math Problem Analysis
Mathematical Concepts
Basic Algebra
Linear Equations
Substitution
Formulas
Simple addition and subtraction
Theorems
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Suitable Grade Level
Grades 5-6