Question

Three consecutive integers are such that when they are taken in increasing order and multiplied by 4,3 and 2 respectively,they and up to 97. find these numbers. ​

Answer 1

Answer:

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Answer 2

Answer:

Hi

Step-by-step explanation:

Hint: Here, we have to find the three consecutive integers. We will assume the smallest of the three consecutive integers to be xx. Using the given information, we will form a linear equation in terms of xx. We will solve the obtained equation to find the value of xx, and hence, the three consecutive integers.

Complete step-by-step answer:

Let the smallest integer of the three consecutive integers be xx.

Therefore, the next two consecutive integers will be x+1x+1 and x+2x+2.

First, we will arrange these in increasing order.

Therefore, we get xx, x+1x+1, and x+2x+2.

Now, we will use the given information to form a linear equation in terms of xx.

The three consecutive integers are multiplied by 2, 3, and 4 respectively.

Multiplying xx by 2, we get 2x2x.

Multiplying x+1x+1 by 3, we get 3(x+1)3(x+1).

Multiplying x+2x+2 by 4, we get 4(x+2)4(x+2).

It is given that the three consecutive integers multiplied by 2, 3, and 4 respectively, add up to 74.

Therefore, we can form the equation

2x+3(x+1)+4(x+2)=742x+3(x+1)+4(x+2)=74

We will solve this equation to get the value of xx.

Multiplying the terms of the expression, we get

⇒2x+3x+3+4x+8=74⇒2x+3x+3+4x+8=74

Adding the like terms of the expression, we get

⇒9x+11=74⇒9x+11=74

Subtracting 11 from both sides of the equation, we get

⇒9x+11−11=74−11⇒9x=63⇒9x+11−11=74−11⇒9x=63

Dividing both sides by 9, we get

⇒9x9=639⇒x=7⇒9x9=639⇒x=7

Therefore, the smallest consecutive integer out of the three numbers is 7.

Substituting x=7x=7 in x+1x+1 and x+2x+2, we get the other two integers as

x+1=7+1=8x+1=7+1=8

x+2=7+2=9x+2=7+2=9

Therefore, the three consecutive integers are 7, 8, and 9.

Note: We have used the distributive property of multiplication to find the products 3(x+1)3(x+1) and 4(x+2)4(x+2). The distributive property of multiplication states that a(b+c)=a⋅b+a⋅ca(b+c)=a⋅b+a⋅c.

We can verify our answer by multiplying 7, 8, 9 by 2, 3, 4 respectively and checking the sum.

Multiplying 7 by 2, we get 14.

Multiplying 8 by 3, we get 24.

Multiplying 9 by 4, we get 36.

The sum of 14, 24, and 36 is 74.

Hence, we have verified the answer.

I hope it helps you