Question

Twice the first number is eleven more than the sum of the other two numbers. The sum of twice the first number and three times the third number is one more than the second number. The second number is equal to the sum of the first number and the third number. Find the three numbers.

Answer 1

let the numbers be x, y, z
2x=y+z+11
2x-y-z=11
2x+3z=y+1
2x-y+3z=1
y=x+z
-x+y-z=0
2x-y-z=11-------------- 1
2x-y+3z =1--------------2
-x+y-z= 0-------------- 3

consider equation 1 &2
Multiply 1 by -1
Multiply 2 by 1
we get
-2x+y+z =-11
2x-y+3z =1




Add the two
4z=-10 -------------4
z==-2.5
consider equation 2 & 3
Multiply 2 by 1
Multiply 3 by 1
we get
2x-y+3z =1
-x+y+-z =0
Add the two
1x+2z= 1-------------5
plug value of z
x-5=1
x=6
plug value of x & z in 1
12-y+2.5=11
y=3.5

Answer 2

One-thirdthird of a number is 11 more than ​one-fourthfourth of the same number.
What is the​ number?