7. (5 points) Given that the ratio of the two-digit number $\overline{\mathrm{ab}}$ to $\overline{\mathrm{ba}}$ is $5: 6$, then $\overline{\mathrm{ab}}=$

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7. (5 points) Given that the ratio of the two-digit number $\overline{\mathrm{ab}}$ to $\overline{\mathrm{b} a}$ is $5: 6$, then $\overline{\mathrm{ab}}=$ $\qquad$ 45 .

【Solution】Solution: Since $(10 a+b):(10 b+a)=5: 6$,
so $(10 a+b) \times 6=(10 b+a) \times 5$
$$
60 a+6 b=50 b+5 a
$$

so $55 a=44 b$
then $a=\frac{4}{5} b$,
so $b$ can only be 5, then $a=4$.
Therefore, $\overline{\mathrm{ab}}=45$.
The answer is: 45.