Jose invests money in two simple interest accounts. He invests twice as much in an account paying 10% as he does in an account paying 7%. If he earns $94.50 in interest in one year from both accounts combined, how much did he invest altogether?
Total Principal in Both Accounts = $
solve for x:
.1(2x) + .07x = 94.50
.1(2x)+.07x=94.50
.2x+.07x=94.50
.27x=94.50
Divide $94.50 by .27 to get X.
x= 350
Solve for 10%
2(350)=700
Add amounts together.
700+350= $1,050
Let's assume that the amount invested in the account paying 7% is x.
According to the problem, Jose invests twice as much in the account paying 10%, so the amount invested in that account is 2x.
The formula to calculate simple interest is: Interest = Principal × Rate × Time.
Using this formula, we can calculate the interest earned from both accounts:
Interest from the account paying 7% = 0.07x
Interest from the account paying 10% = 0.1(2x) = 0.2x
Now we can set up the equation based on the given information:
0.07x + 0.2x = 94.50
Combining like terms, the equation becomes:
0.27x = 94.50
Dividing both sides of the equation by 0.27:
x = 94.50 / 0.27
x ≈ 350
So, he invested approximately $350 in the account paying 7%.
Now, let's calculate the amount invested in the account paying 10%:
2x = 2 * 350 = $700
Therefore, Jose invested a total of $350 + $700 = $1050 altogether.
To find the total amount that Jose invested, we need to set up equations based on the given information.
Let's assume that the amount of money invested in the account paying 7% is x (in dollars).
According to the problem, the amount invested in the account paying 10% is twice the amount invested in the account paying 7%. Therefore, the amount invested in the account paying 10% is 2x (in dollars).
Now, we will calculate the interest earned from each account.
The formula for simple interest is: Interest = Principal x Rate x Time
For the account paying 7%, the interest earned is: (x) x (0.07) x (1) = 0.07x
For the account paying 10%, the interest earned is: (2x) x (0.10) x (1) = 0.20x
The problem states that the total interest earned from both accounts combined is $94.50. So, we can set up the following equation:
0.07x + 0.20x = 94.50
Combining like terms:
0.27x = 94.50
Now, divide both sides of the equation by 0.27 to solve for x:
x = 94.50 / 0.27
x ≈ 350
Therefore, Jose invested approximately $350 in the account paying 7%. Since he invested twice as much in the account paying 10%, he invested approximately $700 in the account paying 10%.
To find the total amount he invested, we can add the amounts invested in both accounts:
Total Principal = $350 + $700
Total Principal = $1050
So, Jose invested a total of $1050.