Find the value of y if 402 y 102 ten - JAMB Mathematics 2023 Question

To find the value of \(y\) if \(402_y = 102_{ten}\), we need to interpret the given expression. The subscript \(y\) indicates that the number is written in base \(y\). The number \(402_y\) can be expressed as:

\[4 \times y^2 + 0 \times y^1 + 2 \times y^0 = 102_{ten}\]

Now, let's solve for \(y\):

\[4y^2 + 2 = 102\]

Subtract 2 from both sides:

\[4y^2 = 100\]

Divide by 4:

\[y^2 = 25\]

Take the square root of both sides:

\[y = 5\]