To buy both a new car and a new house, Tina sought two loans totalling $78,825. The simple interest rate on the first loan was 0.2%, while the simple interest rate on the second loan was 5.0%. At the end of the first year, Tina paid a combined interest payment of $2817.23. What were the amounts of the two loans?
So far I have this but don't know where to go from there:
x + y = 78,825
0.02x + 0.05y = 2817.23
Try harder it is wrong
To buy both a new car and a new house, Tina sought two loans totalling $319,531. The simple interest rate on the first loan was 2.7%, while the simple interest rate on the second loan was 2.6%. At the end of the first year, Tina paid a combined interest payment of $8334.15. What were the amounts of the two loans?
(Points :
To solve this problem, we can use a system of equations with two variables. Let's use x to represent the amount of the first loan and y to represent the amount of the second loan.
From the information given, we know that the total amount of the loans is $78,825, so our first equation is:
x + y = 78,825
Now, let's look at the interest payments. The simple interest rate on the first loan is 0.2%, which can be written as 0.002 in decimal form. The simple interest rate on the second loan is 5%, which can be written as 0.05 in decimal form.
The interest paid on the first loan would be the loan amount (x) multiplied by the interest rate (0.002), so the interest paid on the first loan is 0.002x.
Similarly, the interest paid on the second loan would be the loan amount (y) multiplied by the interest rate (0.05), so the interest paid on the second loan is 0.05y.
According to the problem, the combined interest payment after one year is $2817.23. So our second equation is:
0.002x + 0.05y = 2817.23
Now we have a system of two equations:
x + y = 78,825
0.002x + 0.05y = 2817.23
To find the amounts of the two loans (x and y), we can solve this system of equations.
One way to solve this system is by using the substitution method:
1. Solve one equation for one variable (in terms of the other variable).
2. Substitute this expression into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value of that variable back into any of the original equations to find the value of the other variable.
However, in this case, it might be more convenient to use the elimination method:
1. Multiply both sides of the first equation by a coefficient that will make the coefficients of x in both equations equal. Similarly, multiply both sides of the second equation by a coefficient that will make the coefficients of y in both equations equal.
2. Add or subtract the two equations to eliminate one of the variables.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value of that variable back into any of the original equations to find the value of the other variable.