Answer:
When 27 is added to it, the digits of the number get reversed. We have to find the number. Let the digit in tens place be x and unit place be y. Therefore, the number is 36.
Answer:
Step 1: Use the first equation
+
=
9
a+b=9
Step 2: Use the second equation
10
+
+
27
=
10
+
10a+b+27=10b+a
Rearrange this equation to isolate the terms involving
a and
b:
10
+
+
27
=
10
+
10a+b+27=10b+a
10
−
+
−
10
=
−
27
10a−a+b−10b=−27
9
−
9
=
−
27
9a−9b=−27
−
=
−
3
a−b=−3
Step 3: Solve the system of equations
Now we have two equations:
+
=
9
a+b=9
−
=
−
3
a−b=−3
Add these two equations:
(
+
)
+
(
−
)
=
9
+
(
−
3
)
(a+b)+(a−b)=9+(−3)
+
+
−
=
6
a+b+a−b=6
2
=
6
2a=6
=
3
a=3
Substitute
=
3
a=3 back into the first equation:
3
+
=
9
3+b=9
=
6
b=6
So, the tens digit
a is 3 and the units digit
b is 6.
The Number
The number is:
10
+
=
10
×
3
+
6
=
36
10a+b=10×3+6=36
Step-by-step explanation:
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