Student loans. Brandt's student loans totaled $2500. Part was mde at 3% interest and the rest was made at 2.5%. After the one year Brandt had accumulated $97.50 in interest. What was the amount of each loan? Please HELP ME!!!!!
x and (2500 -x)
.03 x + .025 (2500-x) = 97.50
To solve this problem, let's break it down into two parts: the loan amount at 3% interest and the loan amount at 2.5% interest.
Let's assume the loan amount at 3% interest is x, and the loan amount at 2.5% interest is y. We know that the total loan amount (x + y) is $2500.
Using the formula for interest (Interest = Principal × Rate × Time), we can set up two equations based on the given information:
1) (x * 0.03) + (y * 0.025) = $97.50 (Total accumulated interest)
2) x + y = $2500 (Total loan amount)
Now, we have a system of two equations with two variables. We can solve this system of equations using substitution or elimination method.
Let's use the substitution method:
From equation 2), we can express x in terms of y as x = $2500 - y.
Substituting this value of x in equation 1), we get:
(($2500 - y) * 0.03) + (y * 0.025) = $97.50
Simplifying further, we have:
75 - 0.03y + 0.025y = $97.50
0.005y = $22.50
y = $22.50 / 0.005
y = $4500
Now, substitute the value of y back into equation 2):
x + $4500 = $2500
x = $2500 - $4500
x = -$2000
However, a negative loan amount doesn't make sense in this context. So, there must have been a mistake in the problem. Please verify the given information or check if there's any missing data.