Question

Three consecutive integers are such that when they are taken in increasing order and multiplied by 3, 4 and 5 respectively, they add up to 86. Find these numbers.

Answer 1

Answer:

$\bigstar{\bold{The\:integers\:are\:6,\:7,\:8}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• The integers are consecutive
• Multiplying the integers with 3, 4, 5 respectively give the sum 86

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The integers

$\Large{\underline{\underline{\bf{Solution:}}}}$

➤ Let the integers be x, x +1, x + 2 (since they are consecutive.)

➤ Multiplying with 3, 4, 5 respectively and summing,

   3 × x + 4 (x + 1) + 5 (x + 2) = 86

   3x + 4x + 4 + 5x + 10 = 86

  12x + 14 = 86

  12x = 86 - 14

  12x = 72

   x = 72/12

   x = 6

➤ The first integer = x = 6

➤ The second integer = x + 1 = 6 + 1 = 7

➤ The third integer = x + 2 = 6 + 2 = 8

$\boxed{\bold{The\:integers\:are\:6,\:7,\:8}}$

$\Large{\underline{\underline{\bf{Verification:}}}}$

➛ Multiplying 6,7,8 with 3,4,5 respectively

   6 × 3 + 7 × 4 + 8 × 5

= 18 + 28 + 40

= 86

Hence verified.