Question

6. Three consecutive integers add up to 51. What are these integers?
7. The sum of three consecutive multiples of 8 is 888. Find the multiples
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Answer 1

Answer:

Step-by-step explanation:

6. Let smallest unknown no. be x

Than second no. be x+1

And third no. be x+2

Given-

x+x+1+x+2=51

3x+3=51

3x=51-3

3x=48

x=48/3

x=16

So, three consecutive numbers are 16, 17 and 18

7. Let the first multiple of 8 be 8x.

Therefore the second consecutive multiple of 8 will be 8(x+1)

Also the third consecutive multiple of 8 will be 8(x+2).

It is given that the sum of these three consecutive multiples of 8 is 888

=> 8x + 8(x+1) + 8(x+2) = 888

=> 8x + 8x + 8 + 8x + 16 = 888

=> 24x + 24 = 888

Take 24 on the RHS

=> 24x = 888 - 24

=> x = 864/24

=> x = 36.

Therefore First multiple of 8 be 8x = 8 x 36 = 288

Second Multiple of 8 be 8(x + 1) = 8(36 + 1) = 8 x 37 = 296

Third Multiple of 8 be 8(x + 2) = 8(36 + 2) = 8 x 38 = 304

If we sum up these three multiples i.e (288 + 296 + 304) we get 888.

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Answer 2

Answer:

6. Let the three consecutive integers be x, x+1 and x+2. According to the question,

x + (x+1) + (x+2) = 51

⇒ 3x + 3 = 51

⇒ 3x = 51 – 3

⇒ 3x = 48

⇒ x = 48/3

⇒ x = 16

Thus, the integers are

x = 16

x + 1 = 17

x + 2 = 18

7. Let the three consecutive multiples of 8 be 8x, 8(x+1) and 8(x+2).

According to the question,

8x + 8(x+1) + 8(x+2) = 888

⇒ 8 (x + x+1 + x+2) = 888 (Taking 8 as common)

⇒ 8 (3x + 3) = 888

⇒ 3x + 3 = 888/8

⇒ 3x + 3 = 111

⇒ 3x = 111 – 3

⇒ 3x = 108

⇒ x = 108/3

⇒ x = 36

Thus, the three consecutive multiples of 8 are:

8x = 8 × 36 = 288

8(x + 1) = 8 × (36 + 1) = 8 × 37 = 296

8(x + 2) = 8 × (36 + 2) = 8 × 38 = 304