Question

1.Иван Иванович инвестировал в промысел 5000 долларов. За часть этих денег было договорено 5% дохода в год, а за остальные - 10%. В конце года Иван Иванович получил 400 долларов дохода. Сколько денег было инвестировано за 5% и сколько за 10% дохода? Решите задачу благодаря системе уравнений. 2. Семья положила в банк 2000долларов: часть денег на 3% годовых, остальные - на 4%. В конце года на проценты было насчитано 72 доллара. Сколько денег было положено на 3% и сколько - на 4% годовых? Решите задачу пользуясь системой уравнений.

Answer 1

Могу только первое: х + у = 5000;

5х/100 + 10у/100 = 400

х = 2000; у = 3000

Answer 2

Solution to the First Problem:

To solve the problem of Ivan Ivanovich's investments, we can set up a system of equations based on the given information.

Let's assume: - x as the amount invested at 5% interest - y as the amount invested at 10% interest

We are given the following information: 1. Ivan Ivanovich invested a total of $5000. 2. For part of the money, there was a 5% return, and for the rest, a 10% return. 3. At the end of the year, Ivan Ivanovich received $400 in income.

We can set up the following system of equations: 1. x + y = 5000 (total amount invested is $5000) 2. 0.05x + 0.10y = 400 (income from the investments)

Now, let's 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 the elimination method. Let's use the substitution method.

From the first equation, we can express x in terms of y as x = 5000 - y.

Substituting this value of x into the second equation: 0.05(5000 - y) + 0.10y = 400 250 - 0.05y + 0.10y = 400 0.05y = 150 y = 3000

Now, we can find the value of x: x = 5000 - 3000 x = 2000

Answer to the First Problem:

So, Ivan Ivanovich invested $2000 at a 5% return and $3000 at a 10% return.

Solution to the Second Problem:

For the second problem, we can use a similar approach to set up a system of equations based on the given information.

Let's assume: - a as the amount deposited at 3% interest - b as the amount deposited at 4% interest

We are given the following information: 1. The family deposited a total of $2000. 2. Part of the money was deposited at 3% interest, and the rest was deposited at 4% interest. 3. At the end of the year, $72 in interest was earned.

We can set up the following system of equations: 1. a + b = 2000 (total amount deposited is $2000) 2. 0.03a + 0.04b = 72 (interest earned from the deposits)

Now, let's solve this system of equations to find the values of a and b.

Solving the System of Equations:

We can solve the system of equations using the substitution method or the elimination method. Let's use the substitution method.

From the first equation, we can express a in terms of b as a = 2000 - b.

Substituting this value of a into the second equation: 0.03(2000 - b) + 0.04b = 72 60 - 0.03b + 0.04b = 72 0.01b = 12 b = 1200

Now, we can find the value of a: a = 2000 - 1200 a = 800

Answer to the Second Problem:

So, the family deposited $800 at 3% interest and $1200 at 4% interest.