James invested some money at 12% interest. James also invested $188 more than 4 times that amount at 13%. How much is invested at each rate if Sang receives $2249.57 in interest after one year?
Who is Sang?
How is he involved?
i meant james im sorry.. but i solved the problem on my own thank u tho
To solve this problem, we can break it down into two separate equations.
Let's start by assigning variables to the two unknowns in the problem:
Let X be the amount invested at 12% interest.
Then, 4X + $188 represents the amount invested at 13% interest.
Now we can set up the equations based on the given information and use them to solve for X.
Equation 1: Amount invested at 12% interest:
X × 0.12 = Interest earned at 12%
Equation 2: Amount invested at 13% interest:
(4X + $188) × 0.13 = Interest earned at 13%
Since the total interest earned is $2249.57, we can write the following equation:
Equation 3: Interest earned at 12% + Interest earned at 13% = Total interest earned
X × 0.12 + (4X + $188) × 0.13 = $2249.57
Now we can solve Equation 3 for X:
0.12X + 0.13(4X + $188) = $2249.57
0.12X + 0.52X + 0.13($188) = $2249.57
0.12X + 0.52X + $24.44 = $2249.57
0.64X = $2225.13
X ≈ $3473.89
Therefore, James invested approximately $3473.89 at 12% interest.
And since 4X + $188 represents the amount invested at 13% interest:
4($3473.89) + $188 ≈ $13963.56 + $188 ≈ $14151.56
Therefore, James invested approximately $14151.56 at 13% interest.