A man made two investments,one at 7percent and the other at 8percent interest.the yield on the two investments was le222.if the total amount invested was le3000,how much was invested at each rate ?
If $x was invested at 7%, then the rest (3000-x) was at 8%
Now just add up the interest amounts to find x:
.07x + .08(3000-x) = 222
Tnx bro
To find out how much was invested at each interest rate, let's set up some equations.
Let x be the amount invested at 7% interest rate.
Therefore, the amount invested at 8% interest rate would be (3000 - x) since the total amount invested was le3000.
The yield earned from the investment at 7% interest rate would be:
0.07x
The yield earned from the investment at 8% interest rate would be:
0.08(3000 - x)
According to the problem, the total yield from both investments is le222, so we can set up the equation:
0.07x + 0.08(3000 - x) = 222
Let's solve this equation step by step.
Step 1: Distribute 0.08 to terms inside the parentheses:
0.07x + 0.08 * 3000 - 0.08x = 222
Step 2: Simplify the equation:
0.07x + 240 - 0.08x = 222
Step 3: Combine like terms:
-0.01x + 240 = 222
Step 4: Move 240 to the other side of the equation:
-0.01x = 222 - 240
Step 5: Simplify:
-0.01x = -18
Step 6: Divide both sides of the equation by -0.01:
x = -18 / -0.01
Step 7: Simplify:
x = 1800
So, le1800 was invested at 7% interest rate.
The amount invested at 8% interest rate is:
3000 - x = 3000 - 1800 = le1200.
Therefore, le1800 was invested at 7% interest rate, and le1200 was invested at 8% interest rate.
To determine how much was invested at each interest rate, we can use a system of equations. Let's denote the amount invested at 7% as x, and the amount invested at 8% as y.
From the given information, we know two things:
1. The total amount invested was le3000: x + y = 3000
2. The yield on the two investments was le222: (7/100)x + (8/100)y = 222
We can solve this system of equations to find the values of x and y.
One way to solve this system is by substitution. Rearrange the first equation for x: x = 3000 - y. Now substitute this expression for x in the second equation:
(7/100)(3000 - y) + (8/100)y = 222
Simplify the expression:
21000/100 - (7/100)y + (8/100)y = 222
Combine like terms:
210 - (7/100)y + (8/100)y = 222
Multiply through by 100 to eliminate the decimals:
21000 - 7y + 8y = 22200
Combine like terms again:
y = 22200 - 21000
y = 1200
Now, substitute this value of y back into the first equation to find x:
x + 1200 = 3000
x = 3000 - 1200
x = 1800
Therefore, le1800 was invested at 7%, and le1200 was invested at 8%.