Question

Мати й донька зліпили разом 208 вареників, причому донька працювала 2 години, а мати 3 години. За 1 годину мати робить на 16 вареників більше за доньку. Нехай донька за 1 годину робить X вареників, а мати Y вареників. Яка з наведених систем рівнянь є математичною моделлю ситуації, описаної в умові?

Answer 1

Ответ:

2х+3у=208

у-х=16

должен быть так

Answer 2

Mathematical Model of the Situation

To find the mathematical model that represents the situation described in the question, let's analyze the given information step by step.

1. The daughter worked for 2 hours and made X vareniks per hour. 2. The mother worked for 3 hours and made Y vareniks per hour. 3. Together, they made a total of 208 vareniks.

Based on this information, we can create the following equations:

Equation 1: The daughter's work: 2X = ?

Equation 2: The mother's work: 3Y = ?

Equation 3: The total number of vareniks made: 2X + 3Y = 208

Now, let's solve these equations to find the values of X and Y.

Solving the Equations

To solve the system of equations, we can use substitution or elimination method. Let's use the elimination method here.

Multiplying Equation 1 by 3 and Equation 2 by 2, we get:

6X = ? 6Y = ?

Adding these two equations, we have:

6X + 6Y = ?

Now, let's subtract Equation 3 from this equation:

(6X + 6Y) - (2X + 3Y) = ?

Simplifying, we get:

4X + 3Y = ?

Since we know that 2X + 3Y = 208, we can substitute this value into the equation above:

4X + (2X + 3Y) = ?

Simplifying further, we have:

4X + 2X + 3Y = ?

Combining like terms, we get:

6X + 3Y = ?

Now, we can substitute the value of 208 into the equation:

6X + 3Y = 208

This equation represents the mathematical model of the situation described in the question.

Conclusion

The mathematical model that represents the situation described in the question is:

6X + 3Y = 208