Question

three consecutive integers are such that when they are taken in increasing order and multiplied by 2,3 and 4 respectively, they add up to 74. find these numbers?

Answer 1

ɢɪᴠᴇɴ :-

Three consecutive integers are such that when they are taken in increasing order and multiplied by 2,3 and 4 respectively, they add up to 74.

Tᴏ ғɪɴᴅ :-

• Three consecutive numbers

sᴏʟᴜᴛɪᴏɴ :-

➦ Let the first integer be x

then,

➦ Second integer = (x + 1)

➦ Third integer = ( x + 2)

According to Question :-

• First no × 2 + Second no × 3 + Third no × 4 = 74

• x × 2 + 3(x + 1) + 4(x +2) = 74

➭ 2x + 3x + 3 + 4x + 8 = 74

➭ 9x + 11 = 74

➭ 9x = 74 - 11

➭ 9x = 63

➭ x = 63/9

➭ x = 7

Hence,

• First no = x = 7
• Second no = (x + 1) = 7 - 1 = 8
• Third no = (x + 2) = 7 + 2 = 9

Answer 2

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Given :

Three consecutive integers are such that when they are taken in increasing order and multiplied by 2,3 and 4 respectively, they add up to 74.

Solution :

Let us assume the three consecutive integers to be x, x+1 and x+2.

So,

Let us multiply the three integers with 2,3 and 4 respectively,

we get,

⇒ x*2 = 2x

⇒ (x+1)*3 = 3x + 3

⇒ (x+2)*4 = 4x + 8

Now adding 1, 2 and 3 we get ,

2x +3x+3 +4x+8 =74

9x+11 = 74

9x =74-11

x = 63/9

x = 7

So,

So,the three integers are,

x=7

x+1 = 8

x+2 = 9