Create an equation from the word problem. 'of' indicates multiplication, 'decreased' indicates subtraction, 'increased' indicates addition. Let's use 'x' for the number.
[tex]\sf\dfrac{7}{10}x-13=\dfrac{3}{10}x+13[/tex]
Now solve for 'x'. Subtract 3/10x to both sides:
[tex]\sf\dfrac{4}{10}x-13=13[/tex]
Add 13 to both sides:
[tex]\sf\dfrac{4}{10}x=26[/tex]
Divide 4/10 to both sides or multiply by its reciprocal, 10/4:
[tex]\sf x=\boxed{\sf 65}[/tex]
