A college used a $5000 gift from an alumnus to make two student loans. The first was at 5% annual interest to a nursing student. The second was at 7% to a business major. If the college collected $308 in interest the first year, how much was loaned to each student?

The answer is: the nursing student received a $2,100 loan and the business student received a $2,900 loan

Explanation:

n = nursing student b = business student

step 1:

n + b = 5,000

5%n + 7%b = 308

step 2: we multiply (5%n + 7%b = 308) x - 20

n + b = 5,000

-n - 1.4b = - 6,160

step 3: we subtract

(n - n) + (b - 1.4b) = 5,000 - 6,160

-0.4b = - 1,160

step 4: we divide

-0.4b / - 0.4 = - 1,160 / - 0.4

b = 2,900

step 5: we replace

n + 2,900 = 5,000

n = 2,100