Question

1. The sum of 2 consecutive even numbers is 214. What are the two numbers?

2. The sum of 2 consecutive odd numbers is 243. What are the two numbers?

With reasons.

Answer 1

Solution 1.)

Let the numbers be a and a + 2

According to question,

a + a + 2 = 214

=> 2a + 2 = 214

=> 2a = 212

=> a = 106

First number = 106

Second number = 108
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Solution 2.)

Sum of two odd numbers is always even.

So, This is not possible.

Answer 2

Hey there !!

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1.↪ Let two consecutive even numbers be x and x+2.

x + (x + 2) = 214

2x + 2 = 214

2 ( x + 1 ) = 214

x + 1 = 214 / 2

x + 1 = 107

x = 107 – 1

x = 106

So, x = 106 and x + 2 = 106 + 2 = 108

Thus, two consecutive even numbers are x i.e., 106 and (x+2) i.e, 108.
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2. Sum of two odd numbers is always even. So, this case isn't possible.

Question correction :- The sum of 3 consecutive odd numbers is 243. What are the two numbers?

↪ Let three consecutive odd numbers be x , (x + 2) and (x + 4).

x + ( x + 2 ) + ( x + 4 ) = 243

3x + 6 = 243

3 ( x + 2 ) = 243

x + 2 = 243 / 3

x + 2 = 81

x = 81 – 2

x = 79

So, x = 79 , (x + 2) = 79 + 2 = 81 and (x + 4) = 79 + 4 = 83

Thus, the three consecutive odd numbers are x i.e, 79 , ( x + 2 ) i.e, 81 and ( x + 4 ) = 83.

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Hope my ans.'s satisfactory. (^-^)