The square of (a two-digit number increased by 2) is multiplied by 2 and then…
2025
The square of (a two-digit number increased by 2) is multiplied by 2 and then divided by 5. If twice the result is equal to 500, find the two-digit number.
- A.
45
- B.
23
- C.
87
- D.
47
Attempted by 6 students.
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Correct answer: B
Let n be the two-digit number. Increasing it by 2 and squaring gives (n + 2)^2. This is multiplied by 2 and divided by 5, giving R = (n + 2)^2 x 2 / 5. Twice this result equals 500.
Set up the equation: 2 x ((n + 2)^2 x 2 / 5) = 500.
Simplify: (n + 2)^2 x 4 / 5 = 500, so (n + 2)^2 x 4 = 2500, and (n + 2)^2 = 625.
Take square roots: n + 2 = +/- 25, so n = 23 or n = -27.
Since n must be a positive two-digit number, n = 23.
Verification: (23 + 2)^2 = 25^2 = 625; 625 x 2 / 5 = 250; twice 250 = 500. Hence the number is 23.