Question

Упродовж одного дня громадянин уклав з двома банками кредитні угоди на один рік: із першим банком під 12% річних, із другим - під 15% річних. Загальна сума грошей, отриманих за кредитними угодами, становить 5000 грн. Погашення кредитів здійснюється одноразовим внеском в останній день дії угод. Нарахована сума відсотків за користування кредитами становить 654 грн. Скільки грошей ( у грн ) узяв громадянин під більші відсотки?

Answer 1

654=x*0.12+(5000-x)*0.15

-96=-0.03x

x=3200

значит под 15 процентов он взял 5000-3200=1800

Answer 2

Calculating the Amount Borrowed at Higher Interest Rate

To calculate the amount of money borrowed at the higher interest rate, we can use the information provided about the two credit agreements and the total amount of interest accrued.

The citizen entered into two credit agreements with different banks: - The first bank offered a loan at 12% annual interest rate. - The second bank offered a loan at 15% annual interest rate. - The total amount borrowed through these agreements is 5000 UAH. - The total interest accrued on these loans is 654 UAH.

Let's denote: - x as the amount borrowed at 12% interest rate - y as the amount borrowed at 15% interest rate

The total amount borrowed can be expressed as: x + y = 5000 (1)

The total interest accrued can be expressed as: 0.12x + 0.15y = 654 (2)

We can solve this system of equations to find the values of x and y.

Solving the System of Equations

We can solve the system of equations using the substitution method or any other preferred method. After solving the system of equations, we can find the amount borrowed at the higher interest rate.

Let's proceed with solving the system of equations to find the values of x and y.

Calculation

Using the system of equations: x + y = 5000 (1) 0.12x + 0.15y = 654 (2)

We can solve for x and y to find: x = 3400 UAH y = 1600 UAH

Answer

The citizen borrowed 1600 UAH at the higher interest rate.