Question

find three numbers whos sum is 86, if the first number is three times the difference between the second and the third, and the second number is two more than twice the third.

Answer 1

Answer: 45,28,13

Step-by-step explanation:

Firstly let’s call integer 3

‘x’

Following the information given the following equations can be constructed:

integer 3 = x

integer 2 = 2+2x because 2x represents 2 times integer 3 (which is x) and plus two

integer 1 =3((2x+2)-x) what we have written is the difference between integer 2 (which was (2x+2)) and integer 3 which was x and simply multiply the result of that subtraction by 3

next we can treat them like their own variables almost.

integer 1 + integer 2 + integer 3 =86

so now plug in the equations we have constructed for each integer:

(3((2x+2)-x)) + (2x+2) + x = 86

to make it easier to read please see the image attached below to solve for x

After you have gone through the image I have included you should notice x= 13 great we got one integer! (Integer 3)

now plug in 13 into our integer equations :

integer 2: 2(13)+2= 28

Therefore integer 2 is 28

integer 1: 3((2(13)+2)-(13))=
3((28-13)

3(15)

45

Therefore integer 1 is 45.

and integer 3 is x which as we now know is equal to 13