Of the 5 numbers whose average is 72, the first is
8
1
times the sum of other 4. The first number is __________.
- A60
- B26
- C40
- D80
Solution & Step-by-step Explanation
Let the five numbers be x
1
,x
2
,x
3
,x
4
, and x
5
.
Given that the average of the 5 numbers is 72:
5
x
1
+x
2
+x
3
+x
4
+x
5
=72
x
1
+x
2
+x
3
+x
4
+x
5
=72×5=360
Also, it is given that the first number is
8
1
times the sum of the other 4:
x
1
=
8
1
(x
2
+x
3
+x
4
+x
5
)
8x
1
=x
2
+x
3
+x
4
+x
5
Substitute this in the sum equation:
x
1
+8x
1
=360
9x
1
=360
x
1
=
9
360
=40
1
,x
2
,x
3
,x
4
, and x
5
.
Given that the average of the 5 numbers is 72:
5
x
1
+x
2
+x
3
+x
4
+x
5
=72
x
1
+x
2
+x
3
+x
4
+x
5
=72×5=360
Also, it is given that the first number is
8
1
times the sum of the other 4:
x
1
=
8
1
(x
2
+x
3
+x
4
+x
5
)
8x
1
=x
2
+x
3
+x
4
+x
5
Substitute this in the sum equation:
x
1
+8x
1
=360
9x
1
=360
x
1
=
9
360
=40