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three numbers have a sum of 100. the difference between the two larger numbers is 12. the difference between the two smaller numbers is 2. what are the three numbers​

Respuesta :

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Answer:

28 + 30 +  42   = 100

Step-by-step explanation:

s=small number

s+ (s+2) + (s+2 +12) =100

3s +16 = 100

3s =84

s = 28

small 28

mediam   28+2 = 30

large    30+12 = 42

Answer:

  • The largest number is: 42
  • The middle number is: 30
  • and the smallest number is: 28

Step-by-step explanation:

Let the largest number be x.

Let the middle number be y

and let the smallest number be z.

Now, it is given that:

Three numbers have a sum of 100.

This means that:

     x+y+z=100-------(1)

Also,

The difference between the two larger numbers is 12.

i.e.

x-y=12

i.e.

x=12+y----------(2)

Also

The difference between the two smaller numbers is 2.

i.e.

y-z=2

i.e.

z=y-2---------(3)

On putting the value of x and z from equation (2) and equation (3) into equation (1) we have:

12+y+y+y-2=100

i.e.

10+3y=100

i.e.

3y=100-10

i.e.

3y=90

i.e.

y=90/3

i.e.

y=30

Hence, x=30+12

i.e. x=42

and

z=30-2

i.e.

z=28

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