Question

Mr. Malone is putting money in two saving accounts. Account a started with $200 and he  deposit $15 each month. Account be started with $300 and he deposits $10 each month. 1. Write an equation to represent account A’s $y total after x months. 2. Write an equation to represent account B’s $y total after X months. 3. Solve the system of equations using subtraction. 4. In how many months will the accounts have the same balance? 5. What will this balance be?

Answer 1

In account A:

1.

Mr. Malone is putting $200 first, then he deposits $15 each month

Since y is the total amount of money after x months, then

`y=15x+200\rightarrow(1)`

In account B:

2.

Mr. Malone is putting $300 first, then he deposits $10 each month

Since y is the total amount of money after x months, then

`y=10x+300\rightarrow(2)`

3.

We will subtract equation (1) from equation (2) to eliminate y

`\begin{gathered} y-y=(10x-20x)+(300-200) \\ 0=-10x+100 \end{gathered}`

Add 10x to each side

`\begin{gathered} 0+10x=-10x+10x+100 \\ 10x=100 \end{gathered}`

Divide both sides by 10

`\begin{gathered} (10x)/(10)=(100)/(10) \\ x=10 \end{gathered}`

Substitute x by 10 in equation (1) OR (2) to find y

`\begin{gathered} y=20(10)+200 \\ y=200+200 \\ y=400 \end{gathered}`

The solution of the equations is x = 10, y = 400

4.

After 10 months the accounts will have the same balance

5.

The balance will be $400