If A means +, B means -, C means x, D means \(\div \), then what will come in place of the question mark (?) in the following equation?
18 D 2 A 4 C 5 B 15 = ?
14
Solving the Symbol Substitution Equation
This solution explains how to find the value of the given mathematical expression by substituting specific symbols with arithmetic operators. We need to evaluate the expression \(18 D 2 A 4 C 5 B 15 = ?\).
1. Understanding the Symbol Mappings
The problem defines a specific code where symbols represent mathematical operations:
- A corresponds to addition (\(+\))
- B corresponds to subtraction (\(-\))
- C corresponds to multiplication (\(×\))
- D corresponds to division (\(÷\))
We will use these definitions to rewrite the given equation.
2. The Original Equation
The equation we need to solve is:
\(18 D 2 A 4 C 5 B 15 = ?\)
3. Substituting Symbols with Operators
Replacing each symbol in the equation with its corresponding operator based on the provided key:
- Replace 'D' with \(÷\)
- Replace 'A' with \(+\)
- Replace 'C' with \(×\)
- Replace 'B' with \(-\)
After performing the substitution, the equation transforms into an arithmetic expression:
\(18 \div 2 + 4 \times 5 - 15 = ?\)
4. Applying the Order of Operations (BODMAS/PEMDAS)
To evaluate the arithmetic expression correctly, we must follow the standard order of operations. This is often remembered by the acronym BODMAS:
- Brackets
- Orders (powers and square roots, etc.)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
In our expression, we have division, multiplication, addition, and subtraction. We will perform division and multiplication first, then addition and subtraction.
5. Step-by-Step Calculation
Let's evaluate the expression \(18 \div 2 + 4 \times 5 - 15\) following the BODMAS rule:
- Division: Perform the division first.
\(18 \div 2 = 9\)
The expression now becomes: \(9 + 4 \times 5 - 15\)
- Multiplication: Next, perform the multiplication.
\(4 \times 5 = 20\)
The expression now simplifies to: \(9 + 20 - 15\)
- Addition: Perform the addition.
\(9 + 20 = 29\)
The expression is now: \(29 - 15\)
- Subtraction: Finally, perform the subtraction.
\(29 - 15 = 14\)
6. Final Result
After substituting the symbols and carefully applying the order of operations, the result of the equation \(18 D 2 A 4 C 5 B 15\) is 14.
Similar Questions
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 Operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If ‘A’ stands for ‘\(\div \)', ‘B’ stands for ‘x', ‘C’ stands for ‘+', ‘D’ stands for ‘-', what will come in the place of the question mark '?' in the following equation?
225 B 15 A 15 C 125 D 225 = ?Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 3 - Operations on 3 such as adding /deleting /multiplying etc. to 3 can be performed, Breaking down 3 into | and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(144, 12, 6)
(210, 15, 7)Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 3 - Operations on 3 such as adding /deleting /multiplying etc. to 3 can be performed, Breaking down 3 into | and 3 and then performing mathematical operations on | and 3 is not allowed.)
(9, 6, 56)
(7,8, 58)If 'A' stands for '+', 'B' stands for '×', 'C' stands for '+' and 'D' stands for '-', then what will come in place of the question mark (?) in the following equation?
47 D 25 A 5 C 2 B 9 = ?
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
22 - 5 ÷ 3 + 12 × 3 = ?
Which two numbers should be interchanged to make the given equation correct?
186 - 82 + (129 ÷ 3) − 6 × 8 + (31 - 19) × 2 = 85
(Note: Interchange should be done of entire number and not individual digits of a given number.)
Important Questions from Mathematical Operations
Which two numbers (not digits) should be interchanged to make the given equation correct?
21 × 8 – 18 + (64 ÷ 2) + 32 = 64
The two expressions on either side of the equal sign will have the same value if two numbers on the left-hand side are interchanged and two signs on the right-hand side are interchanged. What are those two numbers (not digits) and the two signs?
9 × 1 ÷ 3 + 8 – 7 = 12 ÷ 3 + 2 × 33 – 13
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 Operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 649 :: 956 : Y
