SOLUTION: Doris invested some money at 5% and some money at 6%. She invested $5,000 more at 6% than she did at 5%. Her total yearly interest from the two investments was $630. How much did D

Question 888592: Doris invested some money at 5% and some money at 6%. She invested $5,000 more at 6% than she did at 5%. Her total yearly interest from the two investments was $630. How much did Doris invest at each rate?
and
The income from a student production was $36,000. The price of a student ticket was $9, and nonstudent tickets were sold at $15 each. Three thousand tickets were sold. How many tickets of each kind were sold?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x= Amount invested at 5.00%
y= Amount invested at 6.00%
5%x+6%y=630
multiply by 100

5 x + 6 y = 63000 .............1
y-x = 5000 .............2
Eliminate y
multiply (1)by -1
Multiply (2) by 6
-5 x -6 y = -63000
-6 x + 6 y = 30000
Add the two equations
-11 x = -33000
/ -11
x = 3000
plug value of x in (1)
5 x + 6 y = 63000
15000 + 6 y = 63000
6 y = 63000 -15000
6 y = 48000
y = 8000
x= 3000 Amount invested at 5%
y= 8000 Amount invested at 6%
----------------
x= Number of student tickets
y= Number of non student tickets

1 x + 1 y = 3000 .............1

9 x + 15 y = 36000 .............2
Eliminate y
multiply (1)by -15
Multiply (2) by 1
-15 x -15 y = -45000
9 x + 15 y = 36000
Add the two equations
-6 x = -9000
/ -6
x = 1500
plug value of x in (1)
1 x + 1 y = 3000
1500 + y = 3000
y = 3000 -1500
y = 1500
y = 1500
x= 1500 Number of student tickets
y= 1500 Number of non student tickets
m.ananth@hotmail.ca

m.ananth@hotmail.ca

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