Which two numbers should be interchanged to make the given equation correct?
$15-26+13\times22÷5=35$
Solving the Equation by Interchanging Numbers
The problem asks us to identify which pair of numbers needs to be swapped in the equation $15-26+13\times22÷5=35$ to make the statement true. We need to test the given options by replacing the numbers and re-evaluating the equation using the standard order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division from left to right, Addition and Subtraction from left to right).
Evaluating the Original Equation
First, let's check the value of the original equation:
$$15-26+13\times22÷5$$
- Division: $22 \div 5 = 4.4$
- Multiplication: $13 \times 4.4 = 57.2$
- Subtraction: $15 - 26 = -11$
- Addition: $-11 + 57.2 = 46.2$
The original equation evaluates to $46.2$, which is not equal to $35$. So, we need to interchange numbers.
Testing Number Interchange Options
Let's test each option by interchanging the specified numbers:
Option 1: Interchange 22 and 26
The equation becomes: $15-22+13\times26÷5$
- Division: $26 \div 5 = 5.2$
- Multiplication: $13 \times 5.2 = 67.6$
- Subtraction: $15 - 22 = -7$
- Addition: $-7 + 67.6 = 60.6$
This result ($60.6$) is not $35$.
Option 2: Interchange 15 and 13
The equation becomes: $13-26+15\times22÷5$
- Division: $22 \div 5 = 4.4$
- Multiplication: $15 \times 4.4 = 66$
- Subtraction: $13 - 26 = -13$
- Addition: $-13 + 66 = 53$
This result ($53$) is not $35$.
Option 3: Interchange 15 and 22
The equation becomes: $22-26+13\times15÷5$
- Division: $15 \div 5 = 3$
- Multiplication: $13 \times 3 = 39$
- Subtraction: $22 - 26 = -4$
- Addition: $-4 + 39 = 35$
This result ($35$) matches the right side of the equation. Therefore, interchanging $15$ and $22$ makes the equation correct.
Option 4: Interchange 35 and 5
Assuming this means replacing the number $5$ in the calculation with $35$: $15-26+13\times35÷5$
- Division: $35 \div 5 = 7$
- Multiplication: $13 \times 7 = 91$
- Subtraction: $15 - 26 = -11$
- Addition: $-11 + 91 = 80$
This result ($80$) is not $35$.
Conclusion
By testing all the options, we found that interchanging the numbers $15$ and $22$ correctly balances the equation.
$$22-26+13\times15÷5 = 35$$
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
