SOLUTION: The ratio of the units digit to the tens digit of a two-digit number is one-half. The tens digit is two more than the units digit. Find the number.

Question 1133070: The ratio of the units digit to the tens digit of a two-digit number is one-half. The tens digit is two more than the units digit. Find the number.
Found 4 solutions by MathLover1, Theo, MathTherapy, Alan3354:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Let be the number.
is the tens digit, is the units digit
The ratio of the units digit to the tens digit, , is. This gives us the proportion

The tens digit is more than the units digit;
substituting in our proportion we have

Cross multiply:

Subtract from each side:

then

so, your two digit number is:

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
u = units digit
t = tens digit

u/t = 1/2.
t = u + 2

therefore, u/t = 1/2 becomes u/(u+2) = 1/2
multiply both sides of the equation by (u+2) to get:
u = 1/2 * (u + 2)
simplify to get:
u = 1/2 * u + 1
subtract 1/2 * u from both sides to get:
u - 1/2 * u = 1
combine like terms to get:
1/2 * u = 1
solve for u to get:
u = 2

t = u + 2 becomes t = 2 + 2 which becomes t = 4

you have t = 4 and u = 2
u/t = 1/2 becomes 2/4 = 1/2 which is true.
t = u + 2 becomes t = 2 + 2 which becomes t = 4 which is true.

solution looks good.
solution is that the tens digit is equal to 4 and the ones digit is equal to 2.
the number is 42.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The ratio of the units digit to the tens digit of a two-digit number is one-half. The tens digit is two more than the units digit. Find the number.

Let the tens digit be T and the units digit, U
We then get:
T = 2U ------- Cross-multiply ------ eq (i)
Also, T = U + 2 ------ eq (ii)
2U = U + 2 ------- Substituting 2U for T in eq (ii)
2U - U = 2
U, or units digit = 2
T = 2(2) ------- Substituting 2 for U in eq (i)
T, or tens digit = 4

For the "life of me," I don't know why @MATHLOVER and @THEO just love to COMPLICATE these math problems when they can be solved much, much easier
and in far less time than they make them seem. I really don't believe anyone having problems with math wants to take FOREVER to solve math problems.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The ratio of the units digit to the tens digit of a two-digit number is one-half.
---------
1/2 is not a ratio. It's a fraction.
1:2 is a ratio.
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