Which two numbers (not digits) should be interchanged to make the given equation correct?
19 + 125 ÷ 25 – 100 ÷ 5 + 4 × 3 = 52

Question

Accepted Answer

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

Original expression: 19 + 125 ÷ 25 – 100 ÷ 5 + 4 × 3

Calculate divisions and multiplication first:
125 ÷ 25 = 5
100 ÷ 5 = 20
4 × 3 = 12

Substitute back:
19 + 5 – 20 + 12

Calculate left to right:
19 + 5 = 24
24 – 20 = 4
4 + 12 = 16

The result is 16, but the equation states it should be 52.

Now, try interchanging the pairs given in options and check which makes the equation equal to 52.

Option 1: Interchange 19 and 4
Expression becomes: 4 + 125 ÷ 25 – 100 ÷ 5 + 19 × 3
Calculate divisions and multiplication:
125 ÷ 25 = 5
100 ÷ 5 = 20
19 × 3 = 57

Expression: 4 + 5 – 20 + 57
Calculate left to right:
4 + 5 = 9
9 – 20 = -11
-11 + 57 = 46
Not equal to 52.

Option 2: Interchange 125 and 100
Expression becomes: 19 + 100 ÷ 25 – 125 ÷ 5 + 4 × 3
Calculate divisions and multiplication:
100 ÷ 25 = 4
125 ÷ 5 = 25
4 × 3 = 12

Expression: 19 + 4 – 25 + 12
Calculate left to right:
19 + 4 = 23
23 – 25 = -2
-2 + 12 = 10
Not equal to 52.

Wait, this is not 52. Let's double-check this option carefully.

Option 3: Interchange 25 and 5
Expression becomes: 19 + 125 ÷ 5 – 100 ÷ 25 + 4 × 3
Calculate divisions and multiplication:
125 ÷ 5 = 25
100 ÷ 25 = 4
4 × 3 = 12

Expression: 19 + 25 – 4 + 12
Calculate left to right:
19 + 25 = 44
44 – 4 = 40
40 + 12 = 52

This equals 52, so option 3 is correct.

Option 4: Interchange 4 and 5
Expression becomes: 19 + 125 ÷ 25 – 100 ÷ 4 + 5 × 3
Calculate divisions and multiplication:
125 ÷ 25 = 5
100 ÷ 4 = 25
5 × 3 = 15

Expression: 19 + 5 – 25 + 15
Calculate left to right:
19 + 5 = 24
24 – 25 = -1
-1 + 15 = 14
Not equal to 52.

Therefore, the correct pair to interchange is 25 and 5 (Option 3).

Answer

Answer

Answer