If the sum of the digits of a certain two-digit number is 15 and reversing its digits increase the number by 9, then the numbers are 7 and 8
Let the two digits numbers be x and y
If the sum of the digits of a certain two-digit number is 15, then;
x + y = 15 .................... 1
If the digits are reversed and increased number by 9
10y + x = 10x + y + 9 ................ 2
From 1, x = 15 - y
Substitute into equation 1 to have:
10y + 15 - y = 10(15-y) + y + 9
9y + 15 = 150 - 9y + 9
18y = 159 - 15
18y = 144
y = 8
Since x = 15 - y
x = 15 - 8
x = 7
This shows that the numbers are 7 and 8
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