Math, asked by anushee5, 1 month ago

Express 64 as the sum of two consecutive natural numbers

Answers

Answered by MissCardiologist

$\huge \fbox \colorbox{orange}{❥Answer࿐ }$

Let 2n + 1 = the first consecutive odd number, where n is an integer.

Let 2n + 3 = the second consecutive odd number.

Since "the sum of the two consecutive odd numbers is 64," we can translate this given information mathematically into the following equation to be solved for n as follows:

(2n + 1) + (2n + 3) = 64

2n + 1 + 2n + 3 = 64

Now, collecting like-terms on the left, we get:

4n + 4 = 64

Now, subtract 4 from both sides of the equation in order to begin isolating the unknown number, n, on the left side:

4n + 4 - 4 = 64 - 4

4n + 0 = 60

4n = 60

Now, divide both sides by 4 in order to isolate n on the left side and thus solve the equation for n:

(4n)/4 = 60/4

(4/4)n = 60/4

(1)n = 15

n = 15

Therefore, ...

2n + 1 = 2(15) + 1

= 30 + 1

= 31 and ...

2n + 3 = 2(15) + 3

= 30 + 3

= 33

CHECK:

(2n + 1) + (2n + 3) = 64

(31) + (33) = 64

31 + 33 = 64

64 = 64

Therefore, the two consecutive odd numbers whose sum is 64 are indeed 31 and 33.

Answered by susumalatha82

Step-by-step explanation:

Let 2n + 1 = the first consecutive odd number, where n is an integer.

Let 2n + 3 = the second consecutive odd number.

Since "the sum of the two consecutive odd numbers is 64," we can translate this given information mathematically into the following equation to be solved for n as follows:

(2n + 1) + (2n + 3) = 64

2n + 1 + 2n + 3 = 64

Now, collecting like-terms on the left, we get:

4n + 4 = 64

Now, subtract 4 from both sides of the equation in order to begin isolating the unknown number, n, on the left side:

4n + 4 - 4 = 64 - 4

4n + 0 = 60

4n = 60

Now, divide both sides by 4 in order to isolate n on the left side and thus solve the equation for n:

(4n)/4 = 60/4

(4/4)n = 60/4

(1)n = 15