The difference between a number consisting of two digits and the number formed by reversing the digits is 45.
There are only 4 such numbers:
61, since 61 - 16 = 45
72, since 72 - 27 = 45
83, since 83 - 38 = 45
94, since 94 - 49 = 45
The sum of three times the tens digit and five times the units is 47. There
are only 2 such numbers:
47, since 3*4 + 5*7 = 12 + 35 = 47
94, since 3*9 + 5*4 = 27 + 20 = 47
So the only 2-digit number having both properties is 94.
But your teacher will not accept that method.
Here's how to work it with algebra:
The difference between a number consisting of two digits and the number formed by reversing the digits is 45.
(10t + u) - (10u + t) = 45
Simplify:
10t + u - 10u - t = 45
Collect like terms:
9t - 9u = 45
Divide through by 9:
t - u = 5
The sum of three times the tens digit and five times the units is 47.
3t + 5u = 47
Solve the system of equations:
t - u = 5
3t + 5u = 47
Solve the first for t:
t - u = 5
t = 5 + u
Substitute in
3t + 5u = 47
3(5 + u) + 5u = 47
15 + 3u + 5u = 47
8u = 32
u = 4
Substitute in
t = 5 + u
t = 5 + 4
t = 9
number = 10t + u = 10(9) + 4 = 94
Edwin
