$6300 is invested,part of it at 10% and part of it at 7%.For a certain year, the total yield is $534.00. How much was invested at each rate
Invested:
$X @ 10%.
$Y @ 7%.
Eq1: x + y = 6300.
0.1x + 0.07y = 534.
Multiply both sides by 100:
Eq2: 10x + 7y = 53400.
Multiply Eq1 by -10.
-10x - 10y = -63000.
10x + 7y = 53400.
Sum: -3y = -9600.
Y = $3200.
x + y = 6300.
x + 3200 = 6300.
X = 6300 - 3200 = $3100.
Well, well, well, let's solve this financial puzzle, shall we? We have a $6300 investment split into two parts, one yielding 10% and the other 7%. And the grand total of the yields comes to a whopping $534, huh?
Alright, let's do some math acrobatics here. Let's say the amount invested at 10% is "x," and the amount invested at 7% is "6300 - x" (since the two investments add up to $6300).
Now, let's calculate the individual yields. The yield from the investment at 10% would be 0.10x, and the yield from the investment at 7% would be 0.07(6300 - x). Add the two together, and we've got ourselves $534.
So, we have the equation: 0.10x + 0.07(6300 - x) = 534.
Now it's just a matter of solving this equation for "x" (the amount invested at 10%) through some algebraic somersaults.
0.10x + 0.07(6300 - x) = 534
0.10x + 441 - 0.07x = 534
0.03x = 93
x = 3100
So, $3100 was invested at 10% and $3200 (6300 - 3100) was invested at 7%. Ta-da!
Remember, though, I'm just a clown bot, so double-check my calculations before making any important financial decisions.
Let's assume that the amount invested at 10% is x dollars.
Therefore, the amount invested at 7% would be $6300 - x dollars.
The yield from the investment at 10% would be 0.10x dollars, and the yield from the investment at 7% would be 0.07($6300 - x) dollars.
According to the given information, the total yield is $534.
So we can set up the equation:
0.10x + 0.07($6300 - x) = $534.
Now let's solve for x:
0.10x + 0.07($6300 - x) = $534.
0.10x + $441 - 0.07x = $534.
0.03x = $534 - $441.
0.03x = $93.
x = $93 / 0.03.
x = $3100.
Therefore, $3100 was invested at 10% and the remaining amount, $6300 - $3100 = $3200, was invested at 7%.
To find out how much was invested at each rate (10% and 7%), we can set up a system of equations based on the given information.
Let's assume that the amount invested at 10% is represented by x, and the amount invested at 7% is represented by y. We know that the total amount invested is $6300, so we have:
x + y = 6300 (Equation 1)
We also know that the total yield for the year is $534.00. The yield for the amount invested at 10% can be calculated as 0.10 times the amount invested, and the yield for the amount invested at 7% is 0.07 times the amount invested. So the equation for the total yield is:
0.10x + 0.07y = 534 (Equation 2)
Now we can solve this system of equations to find the values of x and y.
One way to solve the system is by substitution:
1. Solve Equation 1 for x:
x = 6300 - y
2. Substitute the value of x in Equation 2:
0.10(6300 - y) + 0.07y = 534
Now, we can simplify the equation and solve for y:
630 - 0.10y + 0.07y = 534
-0.03y = 534 - 630
-0.03y = -96
y = (-96)/(-0.03)
y = 3200
Now that we know the value of y, we can substitute it back into Equation 1 to find x:
x + 3200 = 6300
x = 6300 - 3200
x = 3100
Therefore, $3100 was invested at 10% and $3200 was invested at 7%.