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a student takes out two loans totaling $5000 at 4% and 6% annual interest. The total interest after one year is $254. Find the amount of each loan?

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2 Answers

Hi Cheney-
Here is how you solve this problem:
 
Let's call the two loans x and y.  We then know that the two loans total 5000 in value:
 
x + y = 5000
 
We also know that 4% interest of one (x) plus 6% interest of the other (y) equals 254:
 
.04 (x) + .06 (y) = 254
 
We now have a "system of equations."  We can now solve the system using substitution.  This simply means that we are trying to get a single equation that only uses one variable (so we can solve for that variable).  Using the first equation, we can write y in terms of x as follows:
 
y = 5000 - x
 
Substituting this value into the second equation, we get:
 
.04 (x) + .06 (5000 - x) = 254
 
And now, we simply solve for x:
 
.04x + 300 - .06x = 254
 
-.02x = -46
 
x = $2300
 
And using the first equation, x + y = 5000, we can find y:
 
x + y = 5000
 
2300 + y = 5000
 
y = $2700
two equations:
x + y = 5000
0.04x +0.06Y = 254
solving:
X= 5000 - Y
Plugging in second equation
(0.04*(5000-Y) + 0.06Y = 254
200 - 0.04Y + 0.06Y = 254
0.02Y = 54
Y = 54/0.02 = 2700
x = 2300
 

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