Question 309617
find three positive numbers whose sum is 44 if the second number is twice the
 first and the third number is two thirds the first.
:
x + y + z = 44
:
"the second number is twice the first"
y = 2x
:
"the third number is two thirds the first."
z = {{{2/3}}}x
:
Replace y and z in the 1st equation, find x:
x + 2x + {{{2/3}}}x = 44
3x + {{{2/3}}}x = 44
multiply both sides by 3, results:
9x + 2x = 3(44)
11x = 132
x = {{{132/11}}}
x = 12
then
y = 2(12)
y = 24
and
z = {{{2/3}}}(12)
z = 8
:
:
Check solution: 12 + 24 + 8 = 44