Let the five numbers be [tex]a,b,c,d,e,[/tex] so [tex]\frac{a+b+c+d+e}{5}=10\implies a+b+c+d+e=50.[/tex] Suppose we multiply [tex]a[/tex] by 3, so [tex]3a+b+c+d+e=5\cdot 14=70.[/tex] Subtract the first equation from this equation to get [tex]2a=20\implies a=10,[/tex] so [tex]\boxed{10}[/tex] is the number that is multiplied by 3.
