Which two numbers (not digits) should be interchanged to make the given equation correct?

6 × 3 + 8 ÷ 2 + 21 + 5 × 4 – 14 ÷ 7 = 53

Question

Which two numbers (not digits) should be interchanged to make the given equation correct?

6 × 3 + 8 ÷ 2 + 21 + 5 × 4 – 14 ÷ 7 = 53

Accepted Answer

Let's evaluate the original equation step-by-step:

Original equation:
6 × 3 + 8 ÷ 2 + 21 + 5 × 4 – 14 ÷ 7

Calculate each operation using BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction):

6 × 3 = 18  
8 ÷ 2 = 4   
5 × 4 = 20  
14 ÷ 7 = 2

Now substitute back:  
18 + 4 + 21 + 20 - 2 = 61

The left side sums to 61, but the right side is 53, so the equation is incorrect.

Now, try interchanging the pairs given and check which makes the equation equal to 53.

1. Interchange 8 and 4:  
Equation becomes:  
6 × 3 + 4 ÷ 2 + 21 + 5 × 8 – 14 ÷ 7  
Calculate:  
6 × 3 = 18   
4 ÷ 2 = 2  
5 × 8 = 40   
14 ÷ 7 = 2   
Sum:    
18 + 2 + 21 + 40 - 2 = 79 (Not 53)

2. Interchange 3 and 5:   
Equation becomes:           
6 × 5 + 8 ÷ 2 + 21 + 3 × 4 – 14 ÷ 7         
Calculate:       
6 × 5 = 30    
8 ÷ 2 = 4      
3 × 4 = 12       
14 ÷ 7 = 2        
Sum:   
30 + 4 + 21 + 12 - 2 = 65 (Not 53)   
 
3. Interchange 2 and 4:          
Equation becomes:          
6 × 3 + 8 ÷ 4 + 21 + 5 × 2 – 14 ÷ 7        
Calculate:           
6 × 3 = 18  
8 ÷ 4 = 2   
5 × 2 = 10    
14 ÷ 7 = 2   
Sum:    
18 + 2 + 21 + 10 - 2 = 49 (Not 53)

4. Interchange 21 and 14:    
Equation becomes:    
6 × 3 + 8 ÷ 2 + 14 + 5 × 4 – 21 ÷ 7    
Calculate:   
6 × 3 = 18   
8 ÷ 2 = 4   
5 × 4 = 20   
21 ÷ 7 = 3   
Sum:   
18 + 4 + 14 + 20 - 3 = 53 (Correct)

Hence, interchanging 21 and 14 makes the equation correct.

Answer

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