The product of digits of two digit no. Is 24.if its unit's digit exceeds twice its ten's digit by 2;find the number

We could do it algebraically but there are so few choices, let's just take the cases.

"its unit's digit exceeds twice its ten's digit by 2"
---> 14, 26, 38, 4x, the x would have to be 10

so 14, 26, or 38
in which of these do we get a product of 24 from the digits ?

To find the number, we need to set up equations based on the given information.

Let's assume the tens digit of the number is 'x' and the units digit is 'y'. According to the given information:

1. The product of the digits is 24. This can be expressed as: x * y = 24.

2. The unit's digit exceeds twice the ten's digit by 2. This can be expressed as: y = 2x + 2.

Now, we can solve these equations simultaneously to find the values of x and y.

From the first equation (x * y = 24), we can find the possible pairs of (x, y) that satisfy this equation. The pairs are:

(1, 24), (2, 12), (3, 8), (4, 6), (6, 4), (8, 3), (12, 2), (24, 1).

However, we also need to consider the second equation (y = 2x + 2). Let's substitute the values of y from the pairs above into this equation and see which pairs satisfy it:

For (1, 24), (2, 12), (3, 8), (4, 6), (24, 1), y does not equal 2x + 2.

For (6, 4), (8, 3), (12, 2), y equals 2x + 2.

Therefore, the pairs (6, 4), (8, 3), and (12, 2) satisfy both equations. However, we need to find a two-digit number, so we can eliminate the pairs (6, 4) and (12, 2).

The remaining pair is (8, 3). Therefore, the tens digit is 8, and the units digit is 3. Hence, the number is 83.