The sum of two consecutive numbers is 100. Find the numbers.
Answers
Answer:
No two consecutive integers sum to
100
.
49
and
51
are the two consecutive odd integers whose sum is
100
.
Step-by-step explanation:
Assuming the problem is asking what two consecutive integers sum to
100
, then there is no answer, as for any integer
n
, we have
n
+
(
n
+
1
)
=
2
n
+
1
, which is odd, while
100
is even. Thus
2
n
+
1
≠
100
for any integer
n
.
If the problem is asking for two consecutive odd integers whose sum is
100
, we can find them as follows:
Let
n
be the lesser of the two odd integers, then we have
n
+
(
n
+
2
)
=
100
⇒
2
n
+
2
=
100
⇒
2
n
=
98
⇒
n
=
49
Thus the two consecutive odd integers are
49
and
49
+
2
=
51
. Checking, we find that
49
+
51
=
100
, as desired.
Answer:
Let the two consecutive no. be x , x+1
A/q
x + x + 1 = 100
=> 2x + 1 = 100
=> 2x = 100 - 1
=> 2x = 99
=> x = 99/2 = 49.5
Now, 1st no. = x = 49.5
2nd no. = 100 - 49.5
= 50.5 Ans...