A principal of $2500 is invested,part at 8% per annum and the rest at 12% per annum. In a year, the 8% investment interest was doubled the 12% investment interest. How much invested at each rate? Express in the form Ax+By=C
To find the amount invested at each rate, we can set up a system of equations. Let's assume that the amount invested at 8% per annum is x, and the amount invested at 12% per annum is y.
We know that the total principal invested is $2500, so we have the equation:
x + y = 2500 --------------(1)
We also know that the interest earned by the 8% investment is double the interest earned by the 12% investment. In other words, 8% of x is equal to twice the 12% of y. Mathematically, this can be expressed as:
0.08x = 2 * 0.12y
0.08x = 0.24y -------------(2)
To solve this system of equations, we can use the substitution method. Rearrange equation (2) to express x in terms of y:
x = 0.24y / 0.08
x = 3y --------------(3)
Now, substitute equation (3) into equation (1) and solve for y:
3y + y = 2500
4y = 2500
y = 625
Once we have the value of y, we can substitute it back into equation (3) to find x:
x = 3 * 625
x = 1875
So, $1875 was invested at 8% per annum, and $625 was invested at 12% per annum.
Expressing this in the form Ax + By = C, we have:
8% investment: A = 1875, B = 0, C = 2500
12% investment: A = 0, B = 625, C = 2500
Therefore, the expression is:
1875x + 625y = 2500
amount invested at 8% ---- x
amount invested at 12% --- y
x+y = 2500
.08x= 2(.12)y = .24y
times 100
8x = 24y
x = 3y
sub into the 1st
3y + y = 2500
4y = 2500
y = 625
then x = 1875
$1875 were invested at 8% and 625 were invested at 12%
check:
.08(1875) = 150
.12(625) = 75
we can see that 150 is twice 75