Question 190058
Let x = "a number"
Let y = "another number
:
write an equation for each statement:
"One number is 4 times as larger as another."
x = 4y
:
" The sum of their reciprocals is 5/12."
{{{1/x}}} + {{{1/y}}} = {{{5/12}}}
:
From the 1st statement substitute 4y for x in the above equation:
{{{1/(4y)}}} + {{{1/y}}} = {{{5/12}}}
Multiply equation by 12y; results
3 + 12 = 5y
5y = 15
y = {{{15/5}}}
y = 3
:
Remember x = 4y
x = 4(3)
x = 12
:
Check solution in the 2nd statement
{{{1/(12)}}} + {{{1/3}}} = {{{5/12}}}
{{{1/(12)}}} + {{{4/12}}} = {{{5/12}}}