Eva invested a certain amount of money at 5% interest and $1500 more than that amount at 17%. Her total yearly interest was $750. How much did she invest at each rate?
amount invested at 5% --- x
amount invested at 17% ---- x+1500
.05x + .17(x+1500) = 750
times 100
5x + 17(x+1500) = 45000
etc.
can you please let us know where we can invest at 17% ?
To solve this problem, we can use the concept of interest and the formula for simple interest.
Let's assume Eva invested an amount of money, let's call it "x," at 5% interest. According to the problem, she also invested $1500 more than that amount, so the second investment will be x + $1500, and this amount will earn 17% interest.
To calculate the interest earned from each investment, we can use the formula for simple interest:
Interest = Principal × Rate × Time
For the first investment at 5% interest, the interest earned will be 0.05x (since the rate is given as 5% or 0.05). For the second investment at 17% interest, the interest earned will be 0.17(x + $1500) (using the same reasoning).
According to the problem, the total yearly interest was $750, so we can set up the equation:
0.05x + 0.17(x + $1500) = $750
Let's solve this equation step by step:
0.05x + 0.17x + 0.17($1500) = $750
0.22x + $255 = $750
0.22x = $750 - $255
0.22x = $495
Now, divide both sides of the equation by 0.22:
x = $495 / 0.22
x ≈ $2250
So Eva invested approximately $2250 at 5% interest.
To find the amount she invested at 17%, we can substitute this value back into the equation:
x + $1500 = $2250 + $1500 = $3750
Therefore, Eva invested approximately $2250 at 5% interest and $3750 at 17% interest.