Question

Solve the following problem using a system of equations. Show your solving steps using the addition method and state your final answer in a sentence. be sure to check your solution.

$10,800 is divided into two investments, one earning 8% simple interest and the other earning 5% simple interest. After one year, they earn a combined interest of $795. How much was invested in each account?

I have also attached an example chart that also needs to be made as well as the Question I typed out

Here is an example, then you need to solve a similar problem, showing 1. Make a chart or drawing, and state what your variables represent. Be clear and include any units. 2. Write the "easy equation". 3. Write the equation that involves multiplying rates and quantities, then usually add if appropriate (if know total) 4. Solve algebraically. I want you to use the Addition Method, since the Week 7 had you use substitution. 5. State the full solution in sentence form, including any units. EXAMPLE: A 20% acid solution is mixed with a 60% acid solution to make 600 liters of a 50% acid solution. How much of each solution was used? 1. X = amount of 20% solution, in liters X = 600 Y= amount of 60% solution, in liters 20% 60% 50% 20% solution 60% solution 50% solution х 600 Amount of solution in liters Amount of acid in liters 0.20 0.60y For this problem, I like to call the "easy" equation the "no spill" equation. As you pour the two solutions together into the final container, If you don't spill the quantities should add up. 2. x + y = 600 3. The second equation notes that the amount of acid also "adds up". You do not create more acid just by mixing them together! We need to multiply 50% times 600 L to get the acid in final mix. 0.20x + 0.60y = 0.50(600) Writing the system is now done. This is usually the hardest part of these problems! 4. To solve the system by substitution, I like to clear out the decimals from the second equation by multiplying by 10 (if there are fractions, multiply by the LCD). If we multiply the first equation by negative 2 and add, we can solve: - 2x - 2y = - 1200 2x + 6y = 3000 4y = 1800, divide by 4 to get y = 1800/4 = 450, and x = 600 - 450 = 150. 5. SOLUTION: There are 150 L of the 20% acid solution and 450 L of the 60% acid solution.

Answer 1

$8500 invested at 8% simple interest and $2300 invested at 5% simple interest.

Let invested at x = amount 8./ 5./. at invested y = amount 8.1. simple interest 5). simple interest Total Amout 10800 Amount Invested y 795 0.05% 0.08x Interest recieved into two amount so, Here divided $ 10800 رأ x+y = 10800 $ 795 . So And to tal interest recieved Lai , 795 0.08 x + 0.05% equation I multiply the Now solve the by system 8 and egnation دبئ by 100 equation i and subtract them. 86400 8 x + 8y 8a + 5y = 795oo 3y = 6900 y = 6900 3 .. Y = 2300 10800 - 2300 8500