Answer:
The answer is $3,100 at 9%; $4,900 at 11%
Step-by-step explanation:
You can solve this problem with a system of equations, that is, a system that can contain 2 or more equations. In this case, arms 2 linear equations with two variables: x and y. So first you define what your variables are:
- x: amount of money invested in the account with 9% interest
- y: amount of money invested in the account with 11% interest
Now you can define the system of equations. On the one hand you know that in the account that has 11% interest Mr. Brownwood deposited $1800 more than in the other account. In an equation and according to the previously defined variables this means: <em>y=x+1800 Equation (A)</em>
On the other hand, you know Mr. Brownwood earned $ 818 in interest. This means that the sum between the interest generated in the account deposited with 9% interest plus the interest generated in the account deposited with 11% interest is $ 818. And to calculate the amount of money generated by interest you multiply the percentage of interest by the amount deposited. Remember that to convert from percentage to decimal you must divide the number by 100. Then 9% is 0.09 and 11% is 0.11. In summary, considering this, you get the equation:<em> 0.09*x+0.11*y=818 Equation (B)</em>
Now you have both equations with the two variables to solve the system. There are several ways to solve the system. One of the most used ways is substitution, which consists in isolating one of the variables from one of the equations and replacing it in the other equation.
In this case you isolate the variable "y" from equation A, and you get: y=1800+x
Now replace it in equation (B): 0.09*x+0.11*(1800+x)=818
First you apply distributive property, which consists of distributing the multiplication by the terms within the parenthesis:
0.09*x+0.11*1800+0.11*x=818
0.09*x+198+0.11*x=818
Now, we leave the variable x on one side of the equality, in this case the left, and the numbers without the variable on the other side, in this case the right. To pass the numbers from one side of the equality to the other, you must keep in mind that you must use the opposite operation, that is, if the number 198 is adding on one side of the equality, the other side is subtracted:
0.09*x+0.11*x=818-198
Now you perform the corresponding operations. Then you isolate the variable and, and as in the previous case, you pass the number that accompanies the variable on the other side of equality with the opposite operation. In this case it is multiplying and its opposite operation is the division:
0.2*x=620
<em>x=3100</em>
Now you replace this value in either of the two equations, A or B, and solve that equation to get the value of y. So: <em>y=4900</em>
Remembering that x was amount of money invested in the account with 9% interest and y was amount of money invested in the account with 11% interest, you can say that <em>$3100 was the amount invested at 9% and $4900 was the amount invested at 11%</em>
