There are five numbers whose average is 72. If the first number is one-fifth of the sum of the other four numbers, then the first number is:
- A60
- B65
- C54
- D56
Solution & Step-by-step Explanation
Let the five numbers be x
1
,x
2
,x
3
,x
4
, and x
5
.
Given that their average 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
Let the sum of the other four numbers be S, so S=x
2
+x
3
+x
4
+x
5
.
Our equation becomes:
x
1
+S=360
We are also given that the first number is one-fifth of the sum of the other four numbers:
x
1
=
5
1
S⟹S=5x
1
Substitute S=5x
1
into the total sum equation:
x
1
+5x
1
=360
6x
1
=360
x
1
=
6
360
=60
Thus, the first number is 60.
1
,x
2
,x
3
,x
4
, and x
5
.
Given that their average 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
Let the sum of the other four numbers be S, so S=x
2
+x
3
+x
4
+x
5
.
Our equation becomes:
x
1
+S=360
We are also given that the first number is one-fifth of the sum of the other four numbers:
x
1
=
5
1
S⟹S=5x
1
Substitute S=5x
1
into the total sum equation:
x
1
+5x
1
=360
6x
1
=360
x
1
=
6
360
=60
Thus, the first number is 60.