A college used a $5,000 gift from an alumnus to make two student loans. The first was at 5% annual simple interest to a nursing student. The second was at 7% annual simple interest to a business major. If the college collected $310 in interest the first year, how much was loaned to each student?

Question

Walter Walter

Mathematics

13 December, 07:12

A college used a $5,000 gift from an alumnus to make two student loans. The first was at 5% annual simple interest to a nursing student. The second was at 7% annual simple interest to a business major. If the college collected $310 in interest the first year, how much was loaned to each student?

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Answers (1)

Know the Answer?

Abel Adkins · Answer 1

Hello,

Let x the amount allocated to the 1 student

Let y the amount allocated to the 2 student

x+y=5000

5/100 * x + 7/100 * y = 310

==>

5x+7y=31000 (1)

x+y=5000 (2)

(1) - 5 * (2) = = >

2y=6000 = = >y=3000 and x=5000-3000=2000

Proof:

2000+3000=5000

5/100*2000+7/100*3000=100+210=310