Samantha lent her brother some money at 9% simple interest and her sister one-half as much money at 16% interest. If she received a total of 34 cents in interest, then how much did she lend to each one?
$X @ 9% = Her bro. loan.
$X/2 @ 16% = Her sis. loan.
0.09x + 0.16(x/2) = 0.34
0.17x = 0.34
X = 0.34 / 0.17 = $2.00.
X/2 = 2.00 / 2 = $1.00.
chgckjk,
To solve this problem, let's break it down step by step.
Let's assume Samantha lent her brother $x at 9% interest. Since her sister received half as much money, she lent her sister $0.5x.
Now let's calculate the interest earned from lending to her brother. The formula for simple interest is:
Interest = Principal * Rate * Time
In this case, the principal (amount lent) to her brother is x, the rate is 9%, and the time is not given. However, since it is not stated, we assume that the time is 1 year (as we are dealing with simple interest).
So, the interest earned from lending to her brother is:
Interest from brother = x * 9% = 0.09x
Similarly, let's calculate the interest earned from lending to her sister:
Interest from sister = 0.5x * 16% = 0.08x
We are given that the total interest earned is 34 cents, so we can set up the equation:
Interest from brother + Interest from sister = 34 cents
0.09x + 0.08x = 34 (combining like terms)
Now, let's solve the equation:
0.17x = 34 (combining like terms)
x = 34 / 0.17 (dividing both sides by 0.17)
x = 200
So, Samantha lent her brother $200 at 9% interest. Since her sister received half as much money, she lent her sister $0.5 * $200 = $100.
Therefore, Samantha lent $200 to her brother and $100 to her sister.