There are six numbers whose average is 120. If the sixth number is one-fourth of the sum of the remaining five numbers, then the sixth number is:
- A148
- B108
- C144
- D150
Solution & Step-by-step Explanation
Let the six numbers be x
1
,x
2
,x
3
,x
4
,x
5
, and x
6
.
Given that the average of the six numbers is 120:
6
x
1
+x
2
+x
3
+x
4
+x
5
+x
6
=120
x
1
+x
2
+x
3
+x
4
+x
5
+x
6
=120×6=720— (Equation 1)
It is also given that the sixth number is one-fourth of the sum of the remaining five numbers:
x
6
=
4
1
(x
1
+x
2
+x
3
+x
4
+x
5
)
4x
6
=x
1
+x
2
+x
3
+x
4
+x
5
— (Equation 2)
Substitute Equation 2 into Equation 1:
4x
6
+x
6
=720
5x
6
=720
x
6
=
5
720
=144
Therefore, the sixth number is 144.
1
,x
2
,x
3
,x
4
,x
5
, and x
6
.
Given that the average of the six numbers is 120:
6
x
1
+x
2
+x
3
+x
4
+x
5
+x
6
=120
x
1
+x
2
+x
3
+x
4
+x
5
+x
6
=120×6=720— (Equation 1)
It is also given that the sixth number is one-fourth of the sum of the remaining five numbers:
x
6
=
4
1
(x
1
+x
2
+x
3
+x
4
+x
5
)
4x
6
=x
1
+x
2
+x
3
+x
4
+x
5
— (Equation 2)
Substitute Equation 2 into Equation 1:
4x
6
+x
6
=720
5x
6
=720
x
6
=
5
720
=144
Therefore, the sixth number is 144.