Find the value of y if \(402_y = 102_{ten}\)
A
4
B
2
C
5
D
3
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(402_y = 102_ten\)
⇒ 4 x y\(^2\) + 0 x y\(^1\) + 2 x y\(^0\) = 102
⇒ 4y\(^2\) + 0 + 2 x 1 = 102
⇒ 4y\(^2\) + 2 = 102
⇒ 4y\(^2\) = 102 - 2
⇒ 4y\(^2\) = 100
⇒ y\(^2 = \frac {100}{4}\)
⇒ y\(^2\) = 25
∴ y = \sqrt25 = 5
Source: WAEC / JAMB / NECO Classroom Archive (Record #67278)