Two investments totaling
$49,500 produce an annual income of
$1770.
One investment yields
2% per year, while the other yields
4% per year. How much is invested at each rate?
Let's solve this problem step-by-step.
Let's assume the amount invested at 2% per year is x, and the amount invested at 4% per year is y.
According to the problem, the total amount invested is $49,500, so we have the equation:
x + y = 49,500 ----(1)
The annual income from the investments is $1,770, and we know that the income from the investment at 2% is x * 0.02 (2% expressed as a decimal), and the income from the investment at 4% is y * 0.04 (4% expressed as a decimal). So, we can write the second equation:
0.02x + 0.04y = 1,770 ----(2)
To solve the system of equations, we can use substitution or elimination method. Let's use the elimination method.
We can multiply equation (1) by 0.02 to match the coefficient of x in equation (2):
0.02x + 0.02y = 990 ----(3)
Now, let's subtract equation (3) from equation (2) to eliminate x:
0.02x + 0.04y - (0.02x + 0.02y) = 1,770 - 990
This simplifies to:
0.02y - 0.02y = 1,770 - 990
0.02y - 0.02y = 780
0 = 780
This is not a valid equation. It means there is no solution to this system of equations. Therefore, there is no combination of investments that can produce $1,770 annual income with the given amounts of $49,500.
Please double-check the information, or let me know if there are any other details or questions you have.
To solve this problem, we can use a system of equations. Let's assign variables to the unknowns:
Let's say the amount invested at 2% per year is 'x', and the amount invested at 4% per year is 'y'.
According to the problem, the two investments total $49,500, so the first equation is:
x + y = 49,500 -- Equation 1
The second equation relates the annual incomes:
0.02x + 0.04y = 1,770 -- Equation 2
We can now solve this system of equations to find the values of 'x' and 'y'.
One way to solve the system is by using the substitution method. We can start by solving Equation 1 for one of the variables and substituting it into Equation 2.
From Equation 1, we have: x = 49,500 - y
Now we can substitute this expression for 'x' into Equation 2:
0.02(49,500 - y) + 0.04y = 1,770
Now, simplify the equation:
990 - 0.02y + 0.04y = 1,770
0.02y = 1,770 - 990
0.02y = 780
y = 780 / 0.02
y = 39,000
So, the amount invested at 4% per year is $39,000.
Substitute this value back into Equation 1 to find 'x':
x + 39,000 = 49,500
x = 49,500 - 39,000
x = 10,500
Therefore, the amount invested at 2% per year is $10,500.
In summary, $10,500 is invested at 2% per year, while $39,000 is invested at 4% per year.
On two investments totaling $7,500
$
7
,
500
, Kevin lost 2%
2
%
on one and earned 6%
6
%
on the other. If his net annual receipts were $348
$
348
, how much was each investment?
If x is invested at 2%, then
.02x + .04(49500-x) = 1770