Question 611029

Let
You have = $x


5% of x = {{{5x/100}}}


Your sister has = $y


6% of y = {{{6y/100}}}




Together you have
{{{x+y=1000}}}
{{{x=1000-y}}}..............(1)


5% of your money is $6 more than 6% of your sister's money
{{{5x/100=6y/100+6}}}
Multiply by 100 both sides of above equation
{{{(100)(5x/100)=(100)((6y/100)+6)}}}
{{{cross(100)(5x/cross(100))=cross(100)(6y/cross(100))+600)}}}
{{{5x=6y+600}}}..............(2)
Put the value of x from (1) to (2)
{{{5(1000-y)=6y+600}}}
{{{5000-5y=6y+600}}}
{{{5000-600=6y+5y}}}
{{{4400=11y}}}
or
{{{11y=4400}}}
Divide by 11 both sides
{{{11y/11=4400/11}}}
{{{cross(11)y/cross(11)=cross(4400)/cross(11)}}}
{{{y=400}}}

Put the value of y in (1)

{{{x=1000-y}}}
{{{x=1000-400}}}
{{{x=600}}}



You have $600
Your sister has $400


Check
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5% of your money = (600)(5%) = 600(5/100)=(6)(5)=30
6% of your sister money = (400)(6%) = (400)(6/100)=(4)(6)=24 and 6 more = 24+6 = 30