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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?

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?

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