Which two numbers should be interchanged to make the given equation correct?
$14\times5+36-27\div3=85$
Equation Analysis
The problem asks us to identify two numbers within the given equation that need to be interchanged to make the equation mathematically correct. The equation provided is:
$14\times5+36-27\div3=85$
To solve this, we first need to understand the standard order of operations, commonly remembered by the acronyms PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).
Checking Original Equation
Let's evaluate the original equation as it is, following the PEMDAS/BODMAS rules:
- Multiplication: Calculate $14 \times 5$. $14 \times 5 = 70$
- Division: Calculate $27 \div 3$. $27 \div 3 = 9$
- Substitute results: The equation now looks like $70 + 36 - 9$.
- Addition: Calculate $70 + 36$. $70 + 36 = 106$
- Subtraction: Calculate $106 - 9$. $106 - 9 = 97$
The calculation yields 97. However, the equation states the result should be 85. Since $97 \neq 85$, the original equation is incorrect as written.
Interchanging Numbers Verification
We are given options for which numbers to interchange. The correct option suggests swapping 27 and 36. Let's see if this swap makes the equation true.
Replace 36 with 27 and 27 with 36 in the original equation:
New Equation: $14\times5+27-36\div3=85$
Now, let's evaluate this modified equation using the order of operations:
- Multiplication: $14 \times 5 = 70$.
- Division: $36 \div 3 = 12$.
- Substitute results: The equation becomes $70 + 27 - 12$.
- Addition: $70 + 27 = 97$.
- Subtraction: $97 - 12 = 85$.
The result of the calculation is 85. This matches the right-hand side of the equation ($85 = 85$).
Conclusion
By interchanging the numbers 27 and 36, the equation $14\times5+36-27\div3=85$ becomes correct.
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
