Help with this word problem? (416/436 math)?

Question

A certain two-digit number has a value that is a 3 times the sum of its digits. The units digit is one more than three times the tens digit. Find the number.

I am have problems, portraying the two-digit number. If anyone can help me figure this out, and put the procedure of how to do it - thanks a million! I would appreciate it GREATLY!

I have to use a mehod like the elimination method or comparission method.

Okay, thank you but how would I find it if I was given another question like this?

Answer 1

Let u = the units digit and t = the tens digit. Then the value of the number is 10t + u

Three times the sum of the digits would be 3(t+u)

So 10t + u = 3(t+u)

Answer 2

Hayharbr was on the right track, but he didn't finish.

To portray a two digit number is easy. Just write down any two digit number and note its form. If the digits are different, it will look something like 'AB.' If the digits are the same it will look like 'AA.' So, the sum of their digits is either A+B if they are different numbers, or A+A = 2A, if they are the same number.

To find the value of a two digit number is also easy. For any two digit number, the value is:

1 x units digit + 10 x tens digit.

So, for example, the number 43 is: 3 x 1, since 3 represents ones, plus: 4 x 10, since 4 represents the number of groups of ten in the number.

If we let B represent the number of units and A the number of tens, then the value, V, of any two digit number can be expressed this way:

V = 10A + B

Note B is equivalent to 1 x B, since B represents ones.

In your problem, the value of the number is three times the sum of the digits. So we can represent it this way:

V = 10A + B = 3(A + B).

The above equation alone is sufficient to find the values of A and B, because from it we can calculate a ratio of A/B or B/A, which tells us directly what A and B are.

When we perform the algebra on this, which I will leave to you, we get:

7A = 2B --> 7/2 = B/A.

Note that this would have also worked if A = B.

So A = 2 and B = 7, which means your original number was probably 27. But we still need to play with these numbers further to verify this.

Your problem also says that the units digit, B, is equal to 3A + 1. So, as a check, find B with respect to A:

7 = 3(2) + 1, which satisfies the second condition.

Now, sum the digits as a further check:

2 + 7 = 9 = 27/3 = V/3. So, the first condition is also satisfied.

Your number therefore is 27.

Answer 3

The answer is 27. Consider the units digit is u and the tens digit is t. Then put it into algebraic equations.

3(u+t) = x and 3t+1 = u

since u<10, t can only be 0, 1 or 2.

3(0) + 1 = 1
3(1) + 1 = 4
3(2) + 1 = 7

So the possible numbers are 01 (which is not a two-digit number), 14, and 27.

Now 3(1+4) = 15, so 14 cannot be the right answer and 3(2+7) = 27. The answer is 27.

Hope this is what you were looking for.

Answer 4

Let x be the digit in the 10's place, let y be the unit digit.
Then the value of the number is 10x + y.

So 3(x+y) = 10x+y and y = 3x+ 1.

Answer 5

Let u = units digit and t = ten's digit
Then the number is 10t +u
So 10t+u = 3(t+u) <--- Eq 1
and u= 3t+1 <--- Eq 2
Substitute 3t+1 for u in Eq 1 getting:
10t +3t + 1 = 3t +9t +3
t = 2
So u = 3(2) +1 = 7
So the number is 10t +u = 27

Answer 6

27

t - tenths.
u - units.

10t + u = 3(t + u)
10t + u = 3t + 3u
7t = 2u

But u = 3t + 1
7t = 2(3t + 1)
7t = 6t + 2
t = 2

From about:
7t = 2u
7(2) = 2u
14 = 2u
u = 7.

Required number: 27.

Answer 7

Process of elimination:

It has to be a number divisible by three.

The tens digit has to be three or less.

The units digits has to be three or more.

The number has to be less than 100.

Answer 8

10 t +u = 3 (t + u )

Therefore, 7t = 2u

also u = 3t +1.

Therefore, 7t = 2 x (3t +1) = 6t + 2

t = 2

U = 7

tHE NUMBER IS 27.

Answer 9

Here is the equations

10x+y=3*(x+y)

and

y=3x+1

Answer is 27