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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?

### 2 Answers by Expert Tutors

Huzefa K. | Math Teacher|Michigan + Northwestern Law|Perfect Score Math ACT + SATMath Teacher|Michigan + Northwestern Law...
5.0 5.0 (478 lesson ratings) (478)
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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
Francisco E. | Francisco; Civil Engineering, Math., Science, Spanish, Computers.Francisco; Civil Engineering, Math., Sci...
5.0 5.0 (1 lesson ratings) (1)
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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