Apply the problem-solving strategy to find a number when "the sum of three times a number and seven is twenty-five". Let $n$ be the number. "Three times a number" translates to $3n$. The "sum" of this and $7$ is $3n + 7$. "Is twenty-five" translates to $= 25$. This gives the equation $3n + 7 = 25$. To solve, subtract $7$ from both sides to get $3n = 18$. Then divide by $3$ to find $n = 6$. Checking the answer: three times $6$ is $18$, plus $7$ is $25$. Thus, the number is $6$.