Question 971339

Mischa invests ${{{20000}}} into two accounts paying {{{7}}}% and {{{9}}}% annual simple interest respectively. 

in account paying {{{7}}}%={{{0.07}}} Mischa invests ${{{x}}}
and in account paying {{{9}}}%={{{0.09}}} Mischa invests ${{{y}}}


if Mischa invests ${{{20000}}} and earned {{{1550}}} in interest, we have

{{{x+y=20000}}}............eq.1

{{{0.07x+0.09y=1550}}}......eq.2=> both side multiply by {{{100}}}
---------------------------------------

{{{x+y=20000}}}............eq.1=> both side multiply by {{{7}}}
{{{7x+9y=155000}}}......eq.2
---------------------------

{{{7x+7y=140000}}}............eq.1=> both side multiply by {{{7}}}
{{{7x+9y=155000}}}......eq.2
------------------------------subtract eq.1 from eq.2

{{{7x-7x+9y-7y=155000-140000}}}

{{{2y=15000}}}

{{{y=15000/2}}}

{{{highlight(y=7500)}}}

now, find {{{x}}}

{{{x+7500=20000}}}............eq.1

{{{x=20000-7500}}}

{{{highlight(x=12500)}}}

so, Mischa invests {{{highlight(x=12500)}}} in account paying {{{7}}}% , and {{{highlight(y=7500)}}} in account paying {{{9}}}%

check if {{{7}}}% of {{{12500}}} and {{{9}}}% of {{{7500}}} equal to earning {{{1550}}} in interest

{{{7}}}% of {{{12500}}} is {{{12500*0.07=875}}}
{{{9}}}% of {{{7500}}} is {{{7500*0.09=675}}}

then {{{875+675=1550}}} which confirms our solution