Question

A student took out two loans totaling $5000. She borrowed the maximum amount she could at 6% and the remainder at 7% interest per year. At the end of the first year, she owed $310 in interest. How much was loaned at each rate?

The loan at 6% was $____
and the loan at 7% was $___

Answer 1

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 = 25x = 2300

4

200 - 0.04Y + 0.06Y = 254

0.02Y = 54

Y = 54/0.02 = 2700