Answer
The answer is: 3000 dollars was originally deposited into the account that earns a 4% yearly interest and 4500 dollars was originally deposited into the account that earns a 2.5% yearly interest.
Work Step by Step
We assign the variables:
x = amount originally deposited into account A (4% yearly interest)
y = amount originally deposited into account B (2.5% yearly interest)
Step 1:
Find the equations that represent the problem.
We can get the first equation from the wording in the problem.
From "Joyce invests 7500 dollars in two savings accounts", we get
$x+y=7500$
If we solve for x, we get:
$x=7500-y$ -> Eq. 1
We can get the second equation from the wording in the problem.
From "One account earns interest at 4% per year; the other earns 2.5% per year. The total interest earned from both accounts after one year is 232.50 dollars", we get
$0.04x+0.025y=232.5$ -> Eq. 2
Step 2:
Solve the system of equations. Using the substitution method:
-> Substitute Eq. 1 into Eq, 2
$0.04(7500-y)+0.025y=232.5$
$300-0.04y+0.025y=232.5$
$-0.015y=232.5-300$
$-0.015y=-67.5$
$y\frac{-67.5}{-0.015}$
$y=4500$
-> Substitute the value for $y$ into Eq. 1
$x+4500=7500$
$x=7500-4500$
$x=3000$
Step 3:
The answer is: 3000 dollars were originally deposited into the account that earns a 4% yearly interest and 4500 dollars were originally deposited into the account that earns a 2.5% yearly interest.
