Mr. Malone is putting money in two savings accounts. Account A started with $200 and Account B started with $300. Mr. Malone deposits $15 in Account A and $10 in Account B each moth. In how many months will the accounts have the same balance? What will that balance be?
To find out in how many months the accounts will have the same balance, we can set up an equation and solve for the number of months.
Let's denote the number of months as 'm', and the balance in Account A and Account B after 'm' months as 'A(m)' and 'B(m)', respectively.
Given that Account A started with $200 and Account B started with $300, and Mr. Malone deposits $15 in Account A and $10 in Account B each month, we can write the following equations:
A(m) = 200 + 15m
B(m) = 300 + 10m
To find when the accounts will have the same balance, we need to set A(m) equal to B(m) and solve for 'm':
200 + 15m = 300 + 10m
Rearranging the equation:
15m - 10m = 300 - 200
5m = 100
Dividing both sides by 5:
m = 100 / 5
m = 20
Therefore, it will take 20 months for the accounts to have the same balance.
To find the balance at that time, we can substitute the value of 'm' into either A(m) or B(m). Let's use A(m):
A(20) = 200 + 15(20)
A(20) = 200 + 300
A(20) = 500
So, after 20 months, both Account A and Account B will have a balance of $500.