Question

three consecutive integer 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 number​

Answer 1

Answer:

All the three consecutive numbers are 7, 8 and 9 respectively.

Step-by-step explanation:

Let all the three consecutive numbers be x, (x + 1) and (x + 2) respectively.

Given : when we multiplied by 2, 3 and 4 with consecutive numbers in increasing order then it gives the sum 74.

According to question:

2x + 3(x + 1) + 4(x + 2) = 74

→ 2x + 3x + 3 + 4x + 8 = 74

→ 9x + 11 = 74

→ 9x = 74 - 11

→ 9x = 63

→ x = 7

∴ Consecutive numbers are:

First no. = x = 7

Second no. = (x + 1) = (7 + 1) = 8

Third no. = (x + 2) = (7 + 2) = 9

Answer 2

Answer:

Given :-

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

To Find :-

• What are the numbers.

Solution :-

Let, the first consecutive integers be x

Second consecutive integers be x + 1

And, the third consecutive integers will be x + 2

According to the question,

⇒ 2(x) + 3(x + 1) + 4(x + 2) = 74

⇒ 2x + 3x + 3 + 4x + 8 = 74

⇒ 2x + 3x + 4x + 3 + 8 = 74

⇒ 9x + 11 = 74

⇒ 9x = 74 - 11

⇒ 9x = 63

⇒ x = 63/9

➠ x = 7

Hence, the required consecutive integers are,

✧ First consecutive integers = x = 7

✧ Second consecutive integers = x + 1 = 7 + 1 = 8

✧ Third consecutive integers = x + 2 = 7 + 2 = 9

∴ The three consecutive integers are 7, 8 and 9 respectively.

Let's Verify :-

↦ 2(x) + 3(x + 1) + 4(x + 2) = 74

↦ 2x + 3x + 3 + 4x + 8 = 74

Put x = 7 we get,

↦ 2(7) + 3(7) + 3 + 4(7) + 8 = 74

↦ 14 + 21 + 3 + 28 + 8 = 74

↦ 35 + 3 + 28 + 8 = 74

↦ 38 + 36 = 74

↦ 74 = 74

➦ LHS = RHS

Hence, Verified ✔