Answer: the amount of money in the account that earns 10% interest is $500
the amount of money in the account that earns 12% interest is $900
Step-by-step explanation:
Let x represent the amount of money in the account that earns 10% interest.
Let y represent the amount of money in the account that earns 12% interest.
There is $400 more in the account that pays 12% than there is in the other account. This means that
y = x + 400
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering the account that earns 10% interest.
P = x
R = 10
T = 1 year
I = (x × 10 × 1) = 0.1x
Considering the account that earns 12% interest.
P = y
R = 12
T = 1 year
I = (y × 12 × 1) = 0.12x
If the total interest for a year is $158, it means that
0.1x + 0.12y = 158 - - - - - - - - - - -1
Substituting y = x + 400 into equation 1, it becomes
0.1x + 0.12(x + 400) = 158
0.1x + 0.12x + 48 = 158
0.22x = 158 - 48 = 110
x = 110/0.22 = 500
y = x + 400 = 500 + 500
y = 900
