Question

Одно число в 3 раза меньше другого.Если одно из чисел увеличить в 2 раза,то сумма станет равной 42.Найдите числа.Сколько решений имеет эта задача?Как следует изменить формулировку задачи,чтобы решение было единственным?

Answer 1

Первое число - х

Второе число  - 3х

1й вариант

2х + 3х = 42

5х = 42

х = 8,4

3х = 25,2

2й вариант

х + 6х = 42

7х = 42

х = 6

3х = 18

Чтобы не было двух решений написать не "одно их чисел", а "если 2е число увеличить".

Answer 2

задача имеет 2 решения:

1) первое число обозначим через х а второе через 3х, увеличим первое число : 2х

2х+3х=42

5х=42

х=8,4 первое число

2,8 второе разделили на 3

2) второй вариант удвоим 2 число и получится:

х+6х=42

7х=42

х=6

18 второе число

 

Answer 3

Problem Statement

We are given two numbers, where one is three times smaller than the other. If one of the numbers is increased by two times, the sum of the two numbers becomes 42. We need to find the numbers and determine how many solutions this problem has. Additionally, we need to consider how to modify the problem statement to ensure a unique solution.

Solution and Analysis

Let's denote the smaller number as x and the larger number as 3x (since one number is three times smaller than the other). According to the given information, if we increase one of the numbers by two times, the sum becomes 42. This can be represented by the equation: x + 2(3x) = 42

Solving this equation will give us the values of x and 3x.

Calculation

Let's solve the equation: x + 6x = 42 7x = 42 x = 6

So, the smaller number x is 6, and the larger number 3x is 18.

Number of Solutions

This problem has only one solution, as we have found a unique pair of numbers that satisfy the given conditions.

Modifying the Problem Statement

To ensure a unique solution, we can modify the problem statement by adding constraints or specific conditions. For example, we can specify a range for the numbers, introduce a relationship between the numbers, or include additional equations to narrow down the possible solutions.

By adding specific constraints or conditions, we can ensure that the problem has only one solution.

I hope this explanation helps! If you have any further questions or need additional assistance, feel free to ask.