Question

A two digit number is such that 3 times the units digit exceed the tens digit by 14. if the digits are reversed, the value of the number increases by 36. find the number.

Answer 1

To solve this problem, we set up a system of equations to represent the given information. Using substitution, we find that the tens digit is 1 and the units digit is 5. Therefore, the number is 15.

Step-by-step explanation:

To solve this problem, let's set up a system of equations:

Let the original number be represented as AB, where A is the tens digit and B is the units digit.

From the given information, we have:

3B = A + 14 ...(equation 1)

Reversing the digits gives us BA, which is equal to AB + 36:

10B + A = 10A + B + 36

9B - 9A = 36

B - A = 4 ...(equation 2)

We now have a system of equations with equations 1 and 2. We can solve this system using substitution:

Substitute equation 2 into equation 1:

3B = (B - 4) + 14

3B = B + 10

2B = 10

B = 5

Substitute B = 5 back into equation 1:

3(5) = A + 14

15 = A + 14

A = 1

So the number is 15.