Question

The sum of three numbers is $23$. Three times the smallest is $4$ less than the largest, while the sum of the largest and smallest is $16$. Use a linear system in three variables to find the th

Answer 1

let the numbers be x>y>z (largest to smallest)

x+y+z=23   eq1

3z=x-4       

x=3z+4       eq2

x+z=16        eq3

substituting  for x+z in eq1 we get

16+y=23

y=23-16

y=7

substituting for x and y in eq1 we get

3z+4+7+z=23

4z+11=23

4z=23-11=12

z=12/4

z=3

x=3z+4

 x=3(3)+4=9+4

x=13

The three numbers are 13,7 and 3.