three consecutive integers are as such they are taken in increasing order and multiplied by 2,3and4 respectively , they add upto 5

2 thoughts on “three consecutive integers are as such they are taken in increasing order and multiplied by 2,3and4 respectively , they add upto 5”

1. Let the 3 numbers be

   1. x
   2. (x + 1) and
   3. (x + 2)

   ★ According to the question,

   2x + 3(x + 1) + 4(x + 2) = 56

   ➝ 2x + 3x + 3 + 4x + 8 = 56

   ➝ 2x + 3x + 4x + 3 + 8 = 56

   ➝ 9x + 11 = 56

   ➝ 9x = 56 – 11

   ➝ 9x = 45

   ➝ x = 45 ÷ 9

   ➝ x = 5

   We had considered the numbers as x, (x + 1), (x + 2).

   Now that the value of x is found out, substitute the value of x.

   • x = 5
   • (x + 1) = 5 + 1 = 6
   • (x + 2) = 5 + 2 = 7

   ∴ The 3 consecutive numbers are 5, 6, 7

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2. Answer:

   First, let’s name the three consecutive integers.

   Let’s call the first integer: n

   Then the next two integers will be (n+1) and (n+2)

   If we then multiply them as described in the problem and sum these products to 56 we can write an equation as:

   2n+3(n+1)+4(n+2)=56

   We can now solve this equation for n:

   2n+(3×n)+(3×1)+(4×n)+(4×2)=56

   2n+3n+3+4n+8=56

   2n+3n+4n+3+8=56

   (2+3+4)n+(3+8)=56

   9n+11=56

   9n+11−11=56−11

   9n+0=45

   9n=45

   9n/9=45/9

   9n/9 =5

   n=5

   Therefore:

   n+1=5+1=6

   n+2=5+2=7

   The three consecutive integers are: 5, 6, 7

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