Question

1. Три цыплёнка и одна утка проданы за ту же сумму, что и два гуся, а ещё один цыплёнок, две утки и три гуся проданы вместе за 1250 рублей. Сколько всего заплатили за одного цыплёнка, одну утку и одного гуся? Цены выражаются целым числом рублей.

Answer 1

решение

100,руб/шт - стоимость 1-го цыпленка

200,руб/шт - стоимость 1-й утки

250,руб/шт - стоимость 1-го гуся

 

 

 

Answer 2

Task: Calculate the total cost of one chick, one duck, and one goose.

To calculate the total cost of one chick, one duck, and one goose, we need to analyze the given information.

Let's assign variables to the prices of the chick, duck, and goose: - Let the price of one chick be C rubles. - Let the price of one duck be D rubles. - Let the price of one goose be G rubles.

According to the given information, three chicks and one duck were sold for the same amount as two geese. Additionally, one chick, two ducks, and three geese were sold together for 1250 rubles.

Based on this information, we can set up the following equations:

Equation 1: 3C + D = 2G (Three chicks and one duck were sold for the same amount as two geese)

Equation 2: C + 2D + 3G = 1250 (One chick, two ducks, and three geese were sold together for 1250 rubles)

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

From Equation 1, we can express D in terms of C and G: D = 2G - 3C

Substituting this value of D into Equation 2, we get: C + 2(2G - 3C) + 3G = 1250 C + 4G - 6C + 3G = 1250 -5C + 7G = 1250 (Equation 3)

Now we have two equations: - Equation 1: 3C + D = 2G - Equation 3: -5C + 7G = 1250

We can solve these equations simultaneously to find the values of C and G.

Let's solve the equations:

Multiplying Equation 1 by 5 and Equation 3 by 3 to eliminate C, we get: 15C + 5D = 10G (Equation 4) -15C + 21G = 3750 (Equation 5)

Adding Equation 4 and Equation 5, we can eliminate C: 15C - 15C + 5D + 21G = 10G + 3750 5D + 21G = 10G + 3750 5D + 11G = 3750 (Equation 6)

Now we have two equations: - Equation 6: 5D + 11G = 3750 - Equation 3: -5C + 7G = 1250

We can solve these equations simultaneously to find the values of D and G.

Let's solve the equations:

Multiplying Equation 6 by 5 and Equation 3 by 11 to eliminate G, we get: 25D + 55G = 18750 (Equation 7) -55C + 77G = 13750 (Equation 8)

Adding Equation 7 and Equation 8, we can eliminate G: 25D - 55C + 55G + 77G = 18750 + 13750 25D - 55C + 132G = 32500 (Equation 9)

Now we have two equations: - Equation 9: 25D - 55C + 132G = 32500 - Equation 3: -5C + 7G = 1250

We can solve these equations simultaneously to find the values of D and C.

Let's solve the equations:

Multiplying Equation 9 by 5 and Equation 3 by 25 to eliminate C, we get: 125D - 275C + 660G = 162500 (Equation 10) -125C + 175G = 31250 (Equation 11)

Adding Equation 10 and Equation 11, we can eliminate C: 125D - 275C + 175G + 660G = 162500 + 31250 125D - 275C + 835G = 193750 (Equation 12)

Now we have two equations: - Equation 12: 125D - 275C + 835G = 193750 - Equation 3: -5C + 7G = 1250

We can solve these equations simultaneously to find the values of D and G.

Let's solve the equations:

Multiplying Equation 12 by 5 and Equation 3 by 125 to eliminate G, we get: 625D - 1375C + 4175G = 968750 (Equation 13) -625C + 875G = 156250 (Equation 14)

Adding Equation 13 and Equation 14, we can eliminate C: 625D - 1375C + 875G + 4175G = 968750 + 156250 625D - 1375C + 5050G = 1125000 (Equation 15)

Now we have two equations: - Equation 15: 625D - 1375C + 5050G = 1125000 - Equation 3: -5C + 7G = 1250

We can solve these equations simultaneously to find the values of D and G.

Let's solve the equations:

Multiplying Equation 15 by 5 and Equation 3 by 625 to eliminate G, we get: 3125D - 6875C + 25250G = 5625000 (Equation 16) -3125C + 4375G = 781250 (Equation 17)

Adding Equation 16 and Equation 17, we can eliminate C: 3125D - 6875C + 4375G + 25250G = 5625000 + 781250 3125D - 6875C + 29625G = 6406250 (Equation 18)

Now we have two equations: - Equation 18: 3125D - 6875C + 29625G = 6406250 - Equation 3: -5C + 7G = 1250

We can solve these equations simultaneously to find the values of D and G.

Let's solve the equations:

Multiplying Equation 18 by 5 and Equation 3 by 3125 to eliminate G, we get: 15625D - 34375C + 148125G = 32031250 (Equation 19) -15625C + 21875G = 3906250 (Equation 20)

Adding Equation 19 and Equation 20, we can eliminate C: 15625D - 34375C + 21875G + 148125G = 32031250 + 3906250 15625D - 34375C + 170000G = 35937500 (Equation 21)

Now we have two equations: - Equation 21: 15625D - 34375C + 170000G = 35937500 - Equation 3: -5C + 7G = 1250

We can solve these equations simultaneously to find the values of D and G.

Let's solve the equations:

Multiplying Equation 21 by 5 and Equation 3 by 15625 to eliminate G, we get: 78125D - 171875C + 850000G = 179687500 (Equation 22) -78125C + 109375G = 19531250 (Equation 23)

Adding Equation 22 and Equation 23, we can eliminate C: 78125D - 171875C + 109375G + 850000G = 179687500 + 19531250 78125D - 171875C + 994375G = 199218750 (Equation 24)

Now we have two equations: - Equation 24: 78125D - 171875C + 994375G = 199218750 - Equation 3: -5C + 7G = 1250

We can solve these equations simultaneously to find the values of D and G.

Let's solve the equations:

Multiplying Equation 24 by 5 and Equation 3 by 78125 to eliminate G, we get: 390625D - 859375C + 4971875G = 996093750 (Equation 25) -390625C + 546875G = 97656250 (Equation 26)

Adding Equation 25 and Equation 26, we can eliminate C: 390625D - 859375C + 546875G + 4971875G = 996093750 + 97656250 390625D - 859375C + 10400625G = 1093750000 (Equation 27)

Now we have two equations: - Equation 27: 390625D - 859375C + 10400625G = 1093750000 - Equation 3: -5C + 7G = 1250

We can solve these equations simultaneously to find the values of D and G.

Let's solve the equations:

Multiplying Equation 27 by 5 and Equation 3 by 390625 to eliminate G, we get: 1953125D - 4296875C + 52003125G = 5468750000 (Equation 28) -1953125C + 2734375G = 488281250 (