Hard Word Problem?

Question

The units digit of a two digit number is 2 more than 3 times the tens digit. When the digits are reversed, the new tens digit is 4 times the new units digit. Find the number and it's reversal.

Answer 1

u = units
t = tens

tu = number
ut = reversed number

equation =>(1) u = 3t + 2
equation =>(2) u = 4t (because ''u'' replace and ''t'' replace ''u'' inside this equation => t = 4u)


So substituted (2) in the equation (1) we have :

4t = 3t + 2 => t = 2

and put t = 2 in (2) we have => u = 4(2) = 8

So, ''the number'' is tu = 28
and ''the reversed number'' is ut = 82

Answer 2

Just write down what the problem says in words.

Let "ab" be the number so "a" is the tens digit and "b" is the units digit. The units digit is 3 times the tens digit plus 2 so:
b = 3a + 2

Switch it around to "ba". Now the tens digit is 4 times the units digit and "b" has become the tens digit and "a" the units digit.
b = 4a

Two equations with two unknowns. Solve by eliminating one of the variables. This is easy since each are "b = " something. Just set the somethings equal to each other.
4a = 3a + 2
a = 2
b = 8

so the original number is 28 and 8 = 3(2) + 2
the reversed number is 82 and 8 = 4(2)