Which two numbers (not individual digits) should be interchanged to make the given equation correct?
21×5−35+(42÷7)+28=96
- A28 and 35
- B35 and 42
- C21 and 42
- D28 and 21
Solution & Step-by-step Explanation
Let's test the options using the BODMAS rule to find which interchange makes the LHS equal to 96.
The original equation is:
21×5−35+(42÷7)+28=96
Test Option A: Interchange 28 and 35
The equation becomes:
21×5−28+(42÷7)+35
Solve bracket: 42÷7=6
Solve multiplication: 21×5=105
Substitute back: 105−28+6+35
Combine additions: 105+6+35=146
Subtract: 146−28=118
=96
Test Option B: Interchange 35 and 42
The equation becomes:
21×5−42+(35÷7)+28
Solve bracket: 35÷7=5
Solve multiplication: 21×5=105
Substitute back: 105−42+5+28
Combine additions: 105+5+28=138
Subtract: 138−42=96
Since LHS=96=RHS, interchanging 35 and 42 makes the equation correct.
The original equation is:
21×5−35+(42÷7)+28=96
Test Option A: Interchange 28 and 35
The equation becomes:
21×5−28+(42÷7)+35
Solve bracket: 42÷7=6
Solve multiplication: 21×5=105
Substitute back: 105−28+6+35
Combine additions: 105+6+35=146
Subtract: 146−28=118
=96
Test Option B: Interchange 35 and 42
The equation becomes:
21×5−42+(35÷7)+28
Solve bracket: 35÷7=5
Solve multiplication: 21×5=105
Substitute back: 105−42+5+28
Combine additions: 105+5+28=138
Subtract: 138−42=96
Since LHS=96=RHS, interchanging 35 and 42 makes the equation correct.