Question 619174
seven times a two digit number is the same as four times the number obtained on interchanging the digits of the given number.
 if one digit of the given number exceeds the other by 3, find the number.
:
10a + b = "the number"
:
The equation:
7(10a + b) = 4(10b + a)
70a + 7b = 40b + 4a
70a - 4a = 40b - 7b
66a = 33b
:
"one digit of the given number exceeds the other by 3"
We know b is the larger digit from the above equation
b - a = 3
b = (a+3)
:
replace b with (a+3)
66a = 33(a+3)
66a = 33a + 99
66a - 33a = 99
33a = 99
a = 3
:
You can find b, check the solution in the 1st statement