Tìm số tự nhiên có hai chữ số, biết rằng nếu lấy số đó chia cho tổng các chữ số của nó ta được thương bằng 5 và dư 12.

Phương pháp giải

Dựa vào phương pháp phân tích cấu tạo số để trả lời câu hỏi.

Lời giải của GV ufaindo.xyz

Gọi số cần tìm là $\overline {ab} $. Ta có: $\overline {ab} = 5 \times (a + b) + 12$ a + b > 12 $10 \times a + b = 5 \times a + 5 \times b + 12$ $5 \times a = 4 \times b + 12$ (1) Vế phải chia hết cho 4 nên $5 \times a$ chia hết cho 4. Vậy a = 4 hoặc a = 8. - Thay a = 4 vào (1) tìm được b = 2 (loại vì a + b = 6 < 12) - Thay a = 8 vào (1) tìm được b = 7 (thỏa mãn) Vậy số cần tìm là 87.

Báo lỗi - Góp ý

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