Math Problem Statement

Fill in each blank so that the resulting statement is true using the numbers from the lists: First row - 9, 3; Second row - 5, 4. The equation is _ * 4 - _ * 3 = _ - _.

Solution

This problem requires filling in the blanks with the numbers from the two lists to make the equation true. The numbers from the two lists are:

  • First row: 9, 3
  • Second row: 5, 4

The structure of the equation is:
_4_3=__\_ \cdot 4 - \_ \cdot 3 = \_ - \_

Let's analyze the equation.

We need to assign the numbers from the list in such a way that:

  • The first blank multiplied by 4,
  • Minus the second blank multiplied by 3,
  • Should equal the third blank minus the fourth blank.

Let's start by trying the numbers from the list in order.

Possible solution:

If we assign:

  • First blank = 9,
  • Second blank = 5,
  • Third blank = 3,
  • Fourth blank = 4,

Then we get the equation:

9453=349 \cdot 4 - 5 \cdot 3 = 3 - 4

This simplifies to:

3615=136 - 15 = -1

Which is true because:

21=121 = -1

So the correct numbers to fill in the blanks are:

9453=349 \cdot 4 - 5 \cdot 3 = 3 - 4

Would you like further explanation on this solution, or do you have any questions?

Here are five related questions you could explore:

  1. What would happen if we tried the numbers in a different order?
  2. How can we generalize this process for other number sets?
  3. Can this type of equation be solved systematically for any pair of lists?
  4. How does the multiplication affect the outcome in comparison to simple addition or subtraction?
  5. Are there other solutions to this problem using different numbers from the list?

Tip: Always check the equation step by step after substituting values to ensure correctness.

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Math Problem Analysis

Mathematical Concepts

Algebra
Arithmetic Operations
Equations

Formulas

Basic Arithmetic: Multiplication and Subtraction
Equations with unknowns

Theorems

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Suitable Grade Level

Grades 6-8