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📰 Question: What two-digit number is three more than a multiple of 7 and five more than a multiple of 6? 📰 Solution: Let the number be $n$. Then $n \equiv 3 \pmod{7}$ and $n \equiv 5 \pmod{6}$. Solve the system: 📰 From $n \equiv 5 \pmod{6}$, $n = 6k + 5$. Substitute into the first congruence: $6k + 5 \equiv 3 \pmod{7} \Rightarrow 6k \equiv -2 \pmod{7} \Rightarrow 6k \equiv 5 \pmod{7}$. Multiply both sides by the modular inverse of 6 mod 7 (which is 6, since $6 \times 6 = 36 \equiv 1 \pmod{7}$): $k \equiv 5 \times 6 \equiv 30 \equiv 2 \pmod{7}$. Thus, $k = 7m + 2$, and $n = 6(7m + 2) + 5 = 42m + 17$. The two-digit solutions are when $m = 0$: $n = 17$ and $m = 1$: $n = 59$. The smallest is $\boxed{17}$. 📰 Access Your Publix Passport Now Perfect Passwords Hiding Missing Click Here 3922433 📰 A Factory Produces 500 Units Of A Product In 8 Hours If The Production Rate Is Constant How Many Units Are Produced In 15 Hours 4688828 📰 Komasan 7002056 📰 Free Download Windows Mixed Reality Transform Your Pc Into A Vr Powerhouse 2641687 📰 Aldol Addition 2409680 📰 The Shocking Secret Behind Perfect Flight In Every Shuttlecock 3284443 📰 The Unreal Tournament 4334823 📰 Transformers One Sequel 1426996 📰 Calculator Lotto 8038730 📰 Newsradio Cast 9167865 📰 Out From The Furnace 4050794 📰 How Many Calories In A Mcdonalds Hash Brown 1708600 📰 Grocery Outlet App 9813118 📰 Genshin Impact Banners 4970161 📰 Find Flights 2336061