Solving Equation with Symbol Interchange

The problem asks us to evaluate a given equation after changing the meaning of the mathematical symbols. Specifically, we need to swap '+' with '-', and '×' with '÷'.

Original Equation

The original equation provided is:

\( 143 - 28 \times 4 \div 5 + 22 = ? \)

Applying Symbol Interchange Rules

We are given the following rules for interchanging symbols:

• '+' becomes '-'
• '-' becomes '+'
• '×' becomes '÷'
• '÷' becomes '×'

Let's apply these rules to the original equation:

• The '-' between 143 and 28 becomes '+'.
• The '×' between 28 and 4 becomes '÷'.
• The '÷' between 4 and 5 becomes '×'.
• The '+' between 5 and 22 becomes '-'.

So, the new equation after interchanging the symbols is:

\( 143 + 28 \div 4 \times 5 - 22 = ? \)

Solving the New Equation (Order of Operations)

To solve the new equation, we must follow the standard order of operations, often remembered by acronyms like BODMAS or PEMDAS.

• B/P: Brackets/Parentheses
• O/E: Orders/Exponents
• DM: Division and Multiplication (from left to right)
• AS: Addition and Subtraction (from left to right)

Let's solve the equation step-by-step:

\( 143 + 28 \div 4 \times 5 - 22 \)

First, perform the division (leftmost of division/multiplication):

\( 28 \div 4 = 7 \)

Substitute this back into the equation:

\( 143 + 7 \times 5 - 22 \)

Next, perform the multiplication:

\( 7 \times 5 = 35 \)

Substitute this back into the equation:

\( 143 + 35 - 22 \)

Now, perform the addition and subtraction from left to right. First, the addition:

\( 143 + 35 = 178 \)

Substitute this back into the equation:

\( 178 - 22 \)

Finally, perform the subtraction:

\( 178 - 22 = 156 \)

So, the value of the equation after interchanging the symbols is 156.

The steps taken are:

1. Identify the original equation.
2. Understand the symbol interchange rules.
3. Rewrite the equation using the new symbols.
4. Apply the order of operations (BODMAS/PEMDAS) to solve the new equation.
5. Perform division and multiplication from left to right.
6. Perform addition and subtraction from left to right.

Result

The value that comes in place of the question mark is 156.

Revision Table: Equation Solving with Symbol Rules

Additional Information: Logic Based Math Problems

This type of problem is common in logic and reasoning sections of tests. It requires careful attention to the given rules and the correct application of the order of operations. The key is to first translate the equation according to the new rules before attempting to calculate the result. Such problems test your ability to follow instructions precisely and perform basic arithmetic accurately under modified conditions.

Remembering the order of operations (like BODMAS or PEMDAS) is crucial for solving any mathematical expression involving multiple operators.

• BODMAS: Brackets, Order, Division/Multiplication, Addition/Subtraction
• PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

Both acronyms represent the same hierarchy and left-to-right rule for operations at the same level (like division and multiplication, or addition and subtraction).