Question

Решите задачу, составив уравнение быстро даю 30 баллов : У Димы и Саши всего было 570 тенге. На 1/4 своих денег, Дима купил альбом, а Саша на 1/6 своих денег купил книгу. После этого у каждого из них осталось одинаковая сумма денег. Сколько тенге было у Димы первоначально?

Answer 1

Х                 -у Димы
570-х          -у Саши
1/4х            -потратил Дима
1/6(570-х)  -потратил Саша
4/4-1/4=3/4 -3/4х осталось у Димы
6/6-1/6=5/6 -5/6(570-х) осталось у Саши
Составим уравнение
3/4х=5/6(570-х)
3/4х=475-5/6х
19/12х=475
х=300  у Димы
570-300=270 у Саши

Answer 2

Problem Analysis

To solve this problem, we need to find the initial amount of money that Dima had. We are given that the total amount of money Dima and Sasha had together was 570 tenge. Dima spent 1/4 of his money on an album, while Sasha spent 1/6 of her money on a book. After their purchases, they both had the same amount of money left.

Solution

Let's assume that Dima initially had x tenge. Sasha's initial amount of money can be calculated as (570 - x) tenge, since the total amount they had together was 570 tenge.

Dima spent 1/4 of his money on an album, so he had (x - (1/4)x) = (3/4)x tenge left.

Sasha spent 1/6 of her money on a book, so she had ((570 - x) - (1/6)(570 - x)) = (5/6)(570 - x) tenge left.

According to the problem, Dima and Sasha had the same amount of money left, so we can set up the following equation:

(3/4)x = (5/6)(570 - x)

To solve this equation, we can multiply both sides by 24 to eliminate the fractions:

18x = 20(570 - x)

Now, let's simplify and solve for x:

18x = 11400 - 20x 38x = 11400 x = 300

Therefore, Dima initially had 300 tenge.

Answer

Dima initially had 300 tenge.

Source:

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