If '-' means '÷', '÷' means 'x', 'x' means '+' and '$+$' means '-', then what will come in place of the question mark (?) in the following equation? $9 \div 12 \times 450 + 8208 - 18 = ?$
102
Understanding Symbol Substitution Rules
The problem asks us to solve a mathematical equation where the standard arithmetic operators have been redefined. We need to apply the given substitutions correctly and then solve the resulting equation using the order of operations (BODMAS/PEMDAS).
The substitution rules are:
- '-' is replaced by '÷'
- '÷' is replaced by 'x'
- 'x' is replaced by '+'
- '+' is replaced by '-'
Applying Substitutions to the Equation
The original equation is:
$9 \div 12 \times 450 + 8208 - 18 = ?$
Let's apply the substitution rules step-by-step to the original equation:
- Replace '÷' with 'x': $9 \times 12 \times 450 + 8208 - 18$
- Replace 'x' with '+': $9 \times 12 + 450 + 8208 - 18$
- Replace '+' with '-': $9 \times 12 + 450 - 8208 - 18$
- Replace '-' with '÷': $9 \times 12 + 450 - 8208 \div 18$
So, the transformed equation becomes:
$9 \times 12 + 450 - 8208 \div 18 = ?$
Solving the Transformed Equation
Now, we solve the transformed equation using the order of operations (BODMAS/PEMDAS): Brackets, Orders, Division/Multiplication (from left to right), Addition/Subtraction (from left to right).
-
Division: First, perform the division operation.
$8208 \div 18$
To calculate $8208 \div 18$:
$8208 \div 18 = 456$
The equation now is: $9 \times 12 + 450 - 456 = ?$ -
Multiplication: Next, perform the multiplication.
$9 \times 12 = 108$
The equation now is: $108 + 450 - 456 = ?$ -
Addition: Perform the addition.
$108 + 450 = 558$
The equation now is: $558 - 456 = ?$ -
Subtraction: Finally, perform the subtraction.
$558 - 456 = 102$
Therefore, the result of the equation after the symbol substitutions is 102.
Important Questions from Mathematical Operations
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 '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
