Nico is saving money for his college education. He invest some money at 8%, and $1300 less than that amount at 5%. the investments produced a total of $234 intrest in 1 yr.How much did he invest at each rate?
solve for x
.08x + .05(x-1300) = 234
(I suggest multiplying each term by 100
would it be 23 or 2300
test your answer, but $23 wouldn't make a lot of sense, would it?
(did you multiply both sides by 100?)
Can somebody help me i still don't get how to do this?
from my equation :
.08x + .05(x-1300) = 234
times everybody by 100
8x + 5(x-1300) = 23400
8x + 5x - 6500 = 23400
13x = 29900
x = 2300
so larger amount = $2300
smaller investment = 1000
check:
.08(2300) + .05(1000) = 234
To answer this question, we need to set up an equation based on the information provided. Let's break it down step by step:
Let's say Nico invested x dollars at 8% interest. Therefore, he invested (x - 1300) dollars at 5% interest.
The amount of interest earned at 8% can be calculated using the formula: Interest = Principal * Rate * Time. In this case, the interest earned at 8% is 0.08x (8% written as a decimal).
Similarly, the amount of interest earned at 5% is (x - 1300) * 0.05.
According to the problem, the total interest earned is $234. So we can set up the equation:
0.08x + 0.05(x - 1300) = 234
Now we can solve this equation to find the value of x.
0.08x + 0.05x - 65 = 234
Combining like terms:
0.13x - 65 = 234
Adding 65 to both sides of the equation:
0.13x = 234 + 65
0.13x = 299
Now, divide both sides of the equation by 0.13:
x = 299 / 0.13
x ≈ $2,300
So, Nico invested approximately $2,300 at 8% interest.
To find the amount invested at 5%, we subtract $1300 from the total investment at 8%:
$2,300 - $1,300 = $1,000
Therefore, Nico invested $1,000 at 5% interest.