Question

4 йогурта и 3 булочки стоят 60 рублей, а 3 и4 булочки стоят 59 рублей. сколько стоят 5 йогуртов и 6 булочек?

Answer 1

4X + 3Y = 60
3X + 4Y = 59
X - Y = 1 --> X = 1 + Y
4*(1 + Y) + 3Y = 60
4 + 4Y + 3Y = 60
7Y = 56
Y = 8 руб -  стоит одна булочка
Х = 1 + 8 = 9 руб -  стоит один йогурт
5 * 9 + 6 * 8 = 45 + 48 = 93 руб 
Ответ: 5 йогуртов и 6 булочек будут стоить 93 руб.

Answer 2

Problem Analysis

We are given the prices of 4 yogurts and 3 buns, which amount to 60 rubles. We are also given the prices of 3 buns and 4 yogurts, which amount to 59 rubles. We need to determine the cost of 5 yogurts and 6 buns.

Solution

Let's assume the cost of one yogurt is x rubles and the cost of one bun is y rubles.

From the given information, we can form two equations:

Equation 1: 4x + 3y = 60 Equation 2: 3x + 4y = 59

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

Multiplying Equation 1 by 3 and Equation 2 by 4, we get:

Equation 3: 12x + 9y = 180 Equation 4: 12x + 16y = 236

Subtracting Equation 3 from Equation 4, we get:

7y = 56

Dividing both sides of the equation by 7, we find:

y = 8

Substituting the value of y back into Equation 1, we can solve for x:

4x + 3(8) = 60 4x + 24 = 60 4x = 60 - 24 4x = 36 x = 9

Therefore, the cost of one yogurt is 9 rubles and the cost of one bun is 8 rubles.

To find the cost of 5 yogurts and 6 buns, we can multiply the respective prices:

Cost of 5 yogurts = 5 * 9 = 45 rubles Cost of 6 buns = 6 * 8 = 48 rubles

Therefore, 5 yogurts and 6 buns would cost a total of 93 rubles.

Answer

The cost of 5 yogurts and 6 buns is 93 rubles.

Verification

Let's verify our answer using the given information.

The cost of 4 yogurts and 3 buns is 60 rubles. Let's calculate the cost per item:

Cost of 1 yogurt = 60 / 4 = 15 rubles Cost of 1 bun = 60 / 3 = 20 rubles

The cost of 3 buns and 4 yogurts is 59 rubles. Let's calculate the cost per item:

Cost of 1 yogurt = 59 / 4 = 14.75 rubles Cost of 1 bun = 59 / 3 = 19.67 rubles

Since our calculated prices match the given information, we can conclude that our answer of 93 rubles for 5 yogurts and 6 buns is correct.

Conclusion

The cost of 5 yogurts and 6 buns is 93 rubles.