Tìm số có hai chữ số biết rằng khi ta viết thêm số 12 xen giữa hai chữ số của nó ta sẽ được số mới gấp 85 lần số cần tìm.

Phương pháp giải

Dựa vào phương pháp phân tích cấu tạo số để giải bài toán.

Lời giải của GV ufaindo.xyz

Gọi số cần tìm là $\overline {ab} $ Nếu viết số 12 vào giữa hai chữ số của số đó ta được số mới là $\overline {a12b} $ Ta có $\overline {a12b} = \overline {ab} \times 85$ a x 1000 + 120 + b = (a x 10 + b) x 85 (phân tích cấu tạo số) a x 1000 + 120 + b = a x 850 + b x 85 (Bỏ ngoặc ở vế phải) a x 150 + 120 = b x 84 (trừ cả hai vế cho a x 150 + b) a x 25 + 20 = b x 14 (Chia cả 2 vế cho 6) Ta có a x 25 + 20 chia hết cho 5 nên b x 14 chia hết cho 5. $ \Rightarrow $b chia hết cho 5. Mà b không thể bằng 0 vì khi đó a < 0. Do đó b = 5 $ \Rightarrow $a = 2 Thử lại: 2125 = 25 x 85 Vậy số cần tìm là 25.

Báo lỗi - Góp ý

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