Sam 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?
amount lent to brother = x
amount lent to sister = x/2
solve:
.09x + .16(x/2) = 34
Reiny,
Is the answer x=200
Let's assume that Sam lent $x to her brother.
Since her sister received one-half as much money, Sam lent $x/2 to her sister.
The interest earned from lending to her brother at 9% is (x * 9%) = 0.09x.
The interest earned from lending to her sister at 16% is ((x/2) * 16%) = 0.08x.
The total interest earned is the sum of the interest from lending to her brother and sister, which is 0.09x + 0.08x = 0.17x.
According to the problem, the total interest earned is 34 cents, so we can set up the equation 0.17x = 34.
Solving this equation, we get x = 34 / 0.17 = 200.
Therefore, Sam lent $200 to her brother, and she lent $100 to her sister.
To solve this problem, let's assume that Sam lent her brother a certain amount of money, denoted as "X" dollars.
Since Sam lent her sister half as much money as her brother, she lent her sister (1/2)X dollars.
Now, let's calculate the interest received:
For the money lent to her brother at 9% interest, the interest can be calculated using the formula: Interest = Principal * Rate * Time.
The interest earned from her brother's loan would be (X dollars) * (9%) = (9/100)X dollars.
Similarly, for the money lent to her sister at 16% interest, the interest earned would be [(1/2)X dollars] * (16%) = (8/100)X dollars.
Given that the total interest received from both loans is 34 cents, we can set up the equation:
(9/100)X + (8/100)X = 34 cents.
Adding the two terms on the left-hand side:
(17/100)X = 34 cents.
To solve for X, we divide both sides of the equation by (17/100):
X = (34 cents) / (17/100) = (34 cents) * (100/17) = 200 cents = $2.
Therefore, Sam lent her brother $2, which means she lent her sister half as much, or $1.
So, Sam lent $2 to her brother and $1 to her sister.