Final answer:
To find how much was loaned to each student, we can set up a system of equations using the information given. Solving this system will give us the amounts loaned to the nursing student and the business major.
Step-by-step explanation:
To solve this problem, we need to set up a system of equations. Let's assume that the amount loaned to the nursing student is x dollars and the amount loaned to the business major is y dollars.
We know that the first loan was made at 5% annual simple interest, so the interest can be calculated as x * 0.05. Similarly, the second loan was made at 7% interest, so the interest can be calculated as y * 0.07.
We also know that the college collected $310 in interest in the first year, so we can write the equation:
x * 0.05 + y * 0.07 = 310
Finally, we know that the total loan amount was $5000, so we can write another equation:
x + y = 5000
Now we can solve this system of equations to find the values of x and y.
By substituting one equation into another, we can rewrite the second equation as:
x = 5000 - y
Substituting this value of x into the first equation, we get:
(5000 - y) * 0.05 + y * 0.07 = 310
Simplifying and solving for y, we find that y is approximately $2,000. Substituting this value back into the equation x + y = 5000, we can find that x is approximately $3,000.
Therefore, $3,000 was loaned to the nursing student and $2,000 was loaned to the business major