christine5 said:
A certain two digit number is 2 more than 3 times the units digit. If the digits of the number are reversed, the resulting number is 24 less than 4 times the original number. Find the original number. Here is what I have:
10t + u = 3u + 2
How did you arrive at this equation? For what do the variables stand?
I will guess that "t" is the original "tens" digit and that "u" is the original "units" digit, so
the original number was 10t + u.
If so, then the equation above would appear to
represent "(the original number) is 3*(the units digit) plus another (2)".
In the reversed number, the value is 10u + t. This new number is "4*(the original number) less (24)": 10u + t = 4(10t + u) - 24.
This gives you two equations in two unknowns:
. . . . .10t + u = 3u + 2
. . . . .10u + t = 4(10t + u) - 24
These simplify as:
. . . . .5t = u + 1
. . . . .6u + 24 = 39t
Solve the system to find the values of "t" and "u". A good way to start would probably be to solve the first equation for "u=", and then plug this in for "u" in the second equation.
If you get stuck, please reply showing your work and reasoning. Thank you!
