Tìm một số có ba chữ số biết rằng khi viết thêm chữ số 1 vào bên phải số đó thì ta được một số gấp ba lần số có được bằng cách viết thêm chữ số hai vào bên trái số đó
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abc1 = 2abc x 3
abc x10 +1 = (2000 + abc)x3
abc x10 + 1 = 6000 + abc x 3
abc x 7 = 5999
abc = 857
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi số có 5 chữ số cần tìm là x (x ∈ N; 10000 ≤ x ≤ 99999)
Khi thêm 1 vào bên phải số đó ta được số mới là số có 6 chữ số với chữ số hàng đơn vị là 1:
Khi đó số đã cho là số chục và số mới được viết là: 10x + 1.
Khi thêm 1 vào bên trái số đó ta được số mới là số có 6 chữ số với chữ số hàng trăm nghìn là 1
Khi đó số đã cho là số đơn vị và số mới được viết là: 100000 + x.
Theo đề bài ra nếu viết thêm 1 vào bên phải số đó thì được một số lớn gấp ba lần số nhận được khi ta viết thêm 1 vào bên trái số đó nên ta có phương trình
10x + 1 = 3(100000 + x)
⇔ 7x = 299999
⇔ x = 42857 (tmđk)
Vậy số cần tìm là 42857
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi số cần tìm là abcde
Ta có abcde1 = 3.1abcde
<=> 10.abcde + 1 = 300000 + 3.abcde
<=> 7.abcde = 299999 <=> abcde = 42857
![](https://rs.olm.vn/images/avt/0.png?1311)
abc1 = 2abc x 3 abc x10 +1 = (2000 + abc)x3 abc x10 + 1 = 6000 + abc x 3 abc x 7 = 5999 abc = 857 axb=5.(0<a,b<=5) a=5xb. Nen b = 1( vi a <hoac = 5) vay a=5
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi 3 số là abc
theo đb ta có
abc1=3 x 2abc
abc x 10 +1 =3x 2000+3abc
7 abc= 5999
abc=857
vậy số đó là 857
857 dung 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1. khi thêm 4 vào bên trái số đó nghĩa là ta đã cộng thêm với 400
ta được số mới gấp 9 lần số ban đầu
nên 400 gấp 8 lần số ban đầu
hay số ban đầu là \(400:8=50\)
2. khi thêm 9 vào bên trái số đó nghĩa là ta đã cộng thêm với 900
ta được số mới gấp 13 lần số ban đầu
nên 900 gấp 12 lần số ban đầu
hay số ban đầu là \(900:12=75\)
![](https://rs.olm.vn/images/avt/0.png?1311)
khi viết thêm chữ số 2 vào bên trái số có 3 chữ số thì số đó tăng lên 2000 đơn vị
coi số phải tìm là 1 phần thì
số mới là 9 phần như thế
hiệu là 2000
số phải tìm là
2000 : ( 9 - 1 ) = 250
đáp số 250
chắc chắn
![](https://rs.olm.vn/images/avt/0.png?1311)
1,Gọi số cần tìm là ab
Khi viết thêm chữ số 9 vào bên trái ta có : 9ab
Theo bài ra ta có :
ab x 13 = 9ab
ab x 13 = 900 + ab
ab x 13 - ab =900
ab x ( 13 - 1 ) = 900
ab x 12 = 900
ab = 900 : 12
ab = 75
2, Nếu viết thêm chữ số 5 vào bên phải thì số đó sẽ tăng 10 lần và 5 đơn vị
( bạn tự vẽ sơ đồ )
Số cần tìm là : ( 1112 - 5 ) : (10 - 1 ) = 123
ko muốn động não em tự nghĩ nhé