Question

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1) three consecutive integers are such that when they are taken in increasing order & multiplied by 3 4 and 5 respectively they add up to 86. Find these numbers.​

Answer 1

Questions & Answers

CBSE

Mathematics

Grade 10

Solution of Linear Equations

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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.

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Hint: Here, we have to find the three consecutive integers. We will assume the smallest of the three consecutive integers to be x

. Using the given information, we will form a linear equation in terms of x

. We will solve the obtained equation to find the value of x

, and hence, the three consecutive integers.

Complete step-by-step answer:

Let the smallest integer of the three consecutive integers be x

.

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

and x+2

.

First, we will arrange these in increasing order.

Therefore, we get x

, x+1

, and x+2

.

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

.

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

Multiplying x

by 2, we get 2x

.

Multiplying x+1

by 3, we get 3(x+1)

.

Multiplying x+2

by 4, we get 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)=74

We will solve this equation to get the value of x

.

Multiplying the terms of the expression, we get

⇒2x+3x+3+4x+8=74

Adding the like terms of the expression, we get

⇒9x+11=74

Subtracting 11 from both sides of the equation, we get

⇒9x+11−11=74−11⇒9x=63

Dividing both sides by 9, we get

⇒9x9=639⇒x=7

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

Substituting x=7

in x+1

and x+2

, we get the other two integers as

x+1=7+1=8

x+2=7+2=9

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