The sum of 3consecutivenumberis36.find the number
Answers
Answer:
Given let a, b, c be the three numbers
Then according to questions,
a+b+c=6 ...……….(1)
a+2c=7 …………..(2)
3a+b+c=12 …………..(3)
Using the determinant property for finding the value of a,b,c we get
AX=B
⇒X=A
−1
B
⎣
⎢
⎢
⎡
1
1
3
1
0
1
1
2
1
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
a
b
c
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
6
7
12
⎦
⎥
⎥
⎤
where A=
⎣
⎢
⎢
⎡
1
1
3
1
0
1
1
2
1
⎦
⎥
⎥
⎤
Now A
−1
=
∣A∣
adjA
we know A=1(0−2)−1(1−6)+1(1) =−2+5+1
∣A∣=4
and adjA =
⎣
⎢
⎢
⎡
−2
0
2
5
−2
−1
1
+2
−1
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
−2
5
1
0
−2
2
2
−1
−1
⎦
⎥
⎥
⎤
Now
⎣
⎢
⎢
⎡
a
b
c
⎦
⎥
⎥
⎤
=
4
1
⎣
⎢
⎢
⎡
−2
5
1
0
−2
2
2
−1
−1
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
6
7
12
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
a
b
c
⎦
⎥
⎥
⎤
=
4
1
⎣
⎢
⎢
⎡
−12+0+24
30−14−12
6+14−12
⎦
⎥
⎥
⎤
=
4
1
⎣
⎢
⎢
⎡
12
4
8
⎦
⎥
⎥
⎤
Hence a=3,b=1,c=2.
Answer:
11,12&13
Step-by-step explanation:
let the numbers be x, x+1&x+2,
according to question,
x+1+x+2+x=36
3x+3=36
3x=36-3
x=33÷3
x=11
now, x+1=11+1=12
x+2= 2+11=13
Hence, the 3 consecutive numbers whose sum is 36 are 11,12,&13 Respectively.