Question

after your done with asking the tutor about the assignment were does the answers go? i know that it is in the profile but i can't find it.the tens digit of a two-digt number is five more than the units digit. The number itself is equal to the sum of its digits multiplied by 8. Find the number.

Answer 1

Let's write the two-digit number as AB, where A is the tens digit, and B the units. We have:

A = 5 + B (the tens digit of a two-digit number is five more than the units digit)

The number AB can be written as:

10A + B

So, since it equals the sum of its digits multiplied by 8, we have:

10A + B = 8(A + B)

10A + B = 8A + 8B

10A + B - 8A = 8A + 8B - 8A

2A + B = 8B

2A + B - B = 8B - B

2A = 7B

Thus, to find that number, we need to solve the following system of equations:

A = 5 + B

2A = 7B

We can replace A in the second equation with 5 + B, to obtain:

2(5 + B) = 7B

10 + 2B = 7B

10 + 2B - 2B = 7B - 2B

10 = 5B

10/5 = 5B/5

2 = B

B = 2

Now, A is given by:

A = 5 + 2 = 7

Therefore, the number is 72.