Which of the following interchanges of numbers (not digits) would make the given equation correct?

(480 ÷ 0.3 × 5 + 500) / (190 + 9 × 27 ÷ 1.6) = 2

Question

Which of the following interchanges of numbers (not digits) would make the given equation correct?

(480 ÷ 0.3 × 5 + 500) / (190 + 9 × 27 ÷ 1.6) = 2

Accepted Answer

Given equation:
(480 ÷ 0.3 × 5 + 500) / (190 + 9 × 27 ÷ 1.6) = 2

Step 1: Calculate numerator and denominator as is:
Numerator = 480 ÷ 0.3 × 5 + 500
= (480 ÷ 0.3) × 5 + 500
= 1600 × 5 + 500
= 8000 + 500 = 8500

Denominator = 190 + 9 × 27 ÷ 1.6
= 190 + (9 × 27) ÷ 1.6
= 190 + 243 ÷ 1.6
= 190 + 151.875 = 341.875

Ratio = 8500 / 341.875 ≈ 24.86 ≠ 2

Step 2: Check each interchange:

Option 1: Swap 500 and 190
Numerator = 480 ÷ 0.3 × 5 + 190 = 8000 + 190 = 8190
Denominator = 500 + 9 × 27 ÷ 1.6 = 500 + 151.875 = 651.875
Ratio = 8190 / 651.875 ≈ 12.56 ≠ 2

Option 2: Swap 0.3 and 1.6
Numerator = 480 ÷ 1.6 × 5 + 500 = 300 × 5 + 500 = 1500 + 500 = 2000
Denominator = 190 + 9 × 27 ÷ 0.3 = 190 + 243 ÷ 0.3 = 190 + 810 = 1000
Ratio = 2000 / 1000 = 2 ✔

Option 3: Swap 27 and 480
Numerator = 27 ÷ 0.3 × 5 + 500 = 90 × 5 + 500 = 450 + 500 = 950
Denominator = 190 + 9 × 480 ÷ 1.6 = 190 + 4320 ÷ 1.6 = 190 + 2700 = 2890
Ratio = 950 / 2890 ≈ 0.33 ≠ 2

Option 4: Swap 5 and 9
Numerator = 480 ÷ 0.3 × 9 + 500 = 1600 × 9 + 500 = 14400 + 500 = 14900
Denominator = 190 + 5 × 27 ÷ 1.6 = 190 + 135 ÷ 1.6 = 190 + 84.375 = 274.375
Ratio = 14900 / 274.375 ≈ 54.3 ≠ 2

Therefore, only option 2 (swapping 0.3 and 1.6) makes the equation correct.

Answer

Answer

Answer