SOLUTION: I need to write an equation and solve for the following: Together my sister and I have $1000. If 5% of my money is $6 more than 6% of my sister's money, how many dollars does m

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: I need to write an equation and solve for the following: Together my sister and I have $1000. If 5% of my money is $6 more than 6% of my sister's money, how many dollars does m      Log On


   

Question 611029: I need to write an equation and solve for the following: Together my sister and I have $1000. If 5% of my money is $6 more than 6% of my sister's money, how many dollars does my sister have?
Thanks,
David R.
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!

Let
You have = $x

5% of x = 5x%2F100

Your sister has = $y

6% of y = 6y%2F100



Together you have
x%2By=1000
x=1000-y..............(1)

5% of your money is $6 more than 6% of your sister's money
5x%2F100=6y%2F100%2B6
Multiply by 100 both sides of above equation
%28100%29%285x%2F100%29=%28100%29%28%286y%2F100%29%2B6%29
cross%28100%29%285x%2Fcross%28100%29%29=cross%28100%29%286y%2Fcross%28100%29%29%2B600%29
5x=6y%2B600..............(2)
Put the value of x from (1) to (2)
5%281000-y%29=6y%2B600
5000-5y=6y%2B600
5000-600=6y%2B5y
4400=11y
or
11y=4400
Divide by 11 both sides
11y%2F11=4400%2F11
cross%2811%29y%2Fcross%2811%29=cross%284400%29%2Fcross%2811%29
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
=====
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