$6300 is invested, part of it at 11% and part of it at 8%. For a certain year, the total yield is $nbsp 597.00 . How much was invested at each rate?
x+y=6300(-11)
0.11x+ 0.08y=597(100)
............................
11x+8y=59700
-11x−11y=−69300
...........................
−3y=−9600
y=3200
........................
x+3200=6300
x=3100
correct
There are some minor flaws in your presentation
x+y=6300(-11) should have been
-11(x+y)=6300(-11) to get
-11x -11y = -69300
0.11x+ 0.08y=597(100) should have said
100(0.11x+ 0.08y)=597(100) to get
11x + 8y = 59700
The way you have it, the left side is not equal to the right side
Let's denote the amount invested at 11% as x and the amount invested at 8% as y.
According to the problem, the first equation is x + y = 6300.
From the given information, the second equation is 0.11x + 0.08y = 597.
To solve the equations, we can multiply the entire second equation by 100 to eliminate the decimals:
11x + 8y = 59700.
Now, let's multiply the first equation by 11:
11x + 11y = 69300.
By subtracting the modified equations, we get:
11x + 8y = 59700
-11x - 11y = -69300
----------------------
-3y = -9600.
Dividing both sides of the equation by -3, we find:
y = 3200.
Substituting the value of y back into the first equation:
x + 3200 = 6300
x = 3100.
Therefore, $3100 was invested at 11% and $3200 was invested at 8%.
To solve this problem, let's assign variables to the unknown amounts:
Let x be the amount invested at 11% and y be the amount invested at 8%.
We are given two pieces of information:
1) The total amount invested is $6300, so we have the equation x + y = 6300.
2) The total yield (interest) from the investments for a certain year is $597. In decimal form, the interest from the amount invested at 11% is 0.11x, and the interest from the amount invested at 8% is 0.08y. So we have the equation 0.11x + 0.08y = 597.
To solve these equations, we can use the method of substitution or elimination.
Using substitution:
1) Rearrange the first equation to express x in terms of y: x = 6300 - y.
2) Substitute x in the second equation with its value from the first equation: 0.11(6300 - y) + 0.08y = 597.
3) Simplify the equation: 693 - 0.11y + 0.08y = 597.
4) Combine like terms: -0.03y = -96.
5) Divide both sides of the equation by -0.03 to solve for y: y = -96 / -0.03 = 3200.
6) Substitute the value of y back into the first equation to solve for x: x + 3200 = 6300.
7) Simplify the equation: x = 6300 - 3200 = 3100.
Therefore, $3100 was invested at 11% and $3200 was invested at 8%.