Question 390882
: find two positive numbers so that twice their sum equals their product and one number is 9 times the other number
:
Let x = one number
then
9x = the other number
:
2(9x + x) = x * 9x
2(10x) = 9x^2
20x = 9x^2
divide both sides by x
20 = 9x
x = {{{20/9}}} is one number
9*{{{20/9}}} = 20  is the other number
:
:
See if this is true in the original statement:
"two positive numbers that twice their sum equals their product"
2({{{20/9}}} + 20) = {{{20/9}}} * 20
2({{{20/9}}} + {{{180/9}}}) = {{{400/9}}}
2({{{200/9}}}) = {{{400/9}}}