What will come in the place of the question mark (?) in the following equation, if '+' and '-' are interchanged and 'x' and '÷' are interchanged? (28 ÷ 4) - (15 x 3) + 48 = ?
Solving the Equation After Symbol Interchange
The problem asks us to find the value that replaces the question mark (?) in the given equation after specific symbol interchanges.
The original equation is:
$$(28 \div 4) - (15 \times 3) + 48 = ?$$
The rules for interchanging symbols are:
- '+' is interchanged with '-'.
- 'x' is interchanged with '÷'.
Let's apply these interchanges to the original equation.
Applying Symbol Interchanges
We need to replace each operator according to the rules:
- The division symbol '÷' becomes 'x'.
- The subtraction symbol '-' becomes '+'.
- The multiplication symbol 'x' becomes '÷'.
- The addition symbol '+' becomes '-'.
Applying these changes to the original equation:
Original: $$(28 \div 4) - (15 \times 3) + 48$$
After interchange: $$(28 \times 4) + (15 \div 3) - 48$$
So, the new equation we need to solve is:
$$(28 \times 4) + (15 \div 3) - 48 = ?$$
Step-by-Step Calculation
Now, we solve the new equation using the standard order of operations (BODMAS/PEMDAS): Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
- Calculate within the brackets:
- First bracket: $$(28 \times 4)$$
Calculation: $ 28 \times 4 = 112 $
- Second bracket: $$(15 \div 3)$$
Calculation: $ 15 \div 3 = 5 $
- First bracket: $$(28 \times 4)$$
- Substitute the results back into the equation:
The equation now becomes: $$112 + 5 - 48$$
- Perform addition and subtraction from left to right:
- Addition: $$112 + 5 = 117$$
- Subtraction: $$117 - 48 = 69$$
Therefore, the value that comes in the place of the question mark is 69.
Final Answer Verification
The original equation was transformed by interchanging '+' with '-' and 'x' with '÷'. The steps involved identifying the operations, applying the interchanges, and then solving the resulting equation using the order of operations (BODMAS/PEMDAS). The calculation yielded 69.
$$(28 \times 4) + (15 \div 3) - 48 = 112 + 5 - 48 = 117 - 48 = 69$$
The value in place of the question mark is 69.
Similar Questions
Which two numbers (not individual digits) should be interchanged to make the given equation correct?
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Important Questions from Bodmas Rule
If 2945 ÷ 19 – 11 × 5 = 29 + a, find the value of a.
DIRECTIONS: What should come in place of the question mark (?) in the following question?
3800 - 22 × 1968 ÷ 48 = ? × 7
Solve: {7.88 × 2 + 2.4 × 5 - 242.4 ÷ 4 + [9.2 × 4 - 2.46 of 3 + (36.3 ÷ 3 - 1.42 × 2)]}
What will come in the place of question mark (?) in the given expression?
(420 ÷ 12 × 35 + 452- 152) = ?2
Evaluate: (13 × 8 - √81 × 6 + 1 ) ÷ (√49 + 72 - 18 × 2 + 19)
