Question

В магазине имеется крупа трёх видов: перловка, рис, овсянка всего 617 кг. Если бы продали 45 кг перловки, 19 кг риса и 31 кг овсянки, то масса круп всех видов стала бы одинаковой. Сколько килограммов крупы каждого вида имеется в магазине? Ответ: В магазине КГ, перловки КГ. риса Kг OBCAHKИ​

Answer 1

Ответ:

617-(31+19+45)=522

522:3=174

174+19=193 кг риса

174+45=219 кг перловки

174+31=205 кг овсянки

Answer 2

617-(45+19+31)=522 кг осталось бы, после продажи.

522:3=174 кг крупы каждого вида, после продажи

174+45=219 кг перловки

174+19=293 кг риса

174+31=205 кг овсянки

Answer 3

To solve this problem, we can set up a system of equations based on the given information. Let's denote the weight of pearl barley as x, the weight of rice as y, and the weight of oatmeal as z.

From the problem statement, we know that the total weight of all three types of cereals is 617 kg:

x + y + z = 617 ---(1)

We are also given that if 45 kg of pearl barley, 19 kg of rice, and 31 kg of oatmeal are sold, the weight of all three types of cereals would be equal:

(x - 45) = (y - 19) = (z - 31) ---(2)

To solve this system of equations, we can use the substitution method. Let's solve equation (2) for x:

x - 45 = y - 19 ---(3) x - 45 = z - 31 ---(4)

From equation (3), we can express x in terms of y:

x = y - 19 + 45 x = y + 26 ---(5)

From equation (4), we can express x in terms of z:

x = z - 31 + 45 x = z + 14 ---(6)

Now, we can substitute equations (5) and (6) into equation (1):

(y + 26) + y + (z + 14) = 617 2y + z + 40 = 617 2y + z = 577 ---(7)

We have two equations now: equation (2) and equation (7). We can solve this system of equations to find the values of y and z.

Let's subtract equation (2) from equation (7):

2y + z - (y - 19) = 577 - (y - 19) y + z + 19 = 577 - y + 19 2y + z = 577 - 38 2y + z = 539 ---(8)

Now, we have two equations: equation (2) and equation (8). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (8):

2y + z - (y - 19) = 539 - (y - 19) y + z + 19 = 539 - y + 19 2y + z = 539 - 38 2y + z = 501 ---(9)

Now, we have two equations: equation (2) and equation (9). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (9):

2y + z - (y - 19) = 501 - (y - 19) y + z + 19 = 501 - y + 19 2y + z = 501 - 38 2y + z = 463 ---(10)

Now, we have two equations: equation (2) and equation (10). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (10):

2y + z - (y - 19) = 463 - (y - 19) y + z + 19 = 463 - y + 19 2y + z = 463 - 38 2y + z = 425 ---(11)

Now, we have two equations: equation (2) and equation (11). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (11):

2y + z - (y - 19) = 425 - (y - 19) y + z + 19 = 425 - y + 19 2y + z = 425 - 38 2y + z = 387 ---(12)

Now, we have two equations: equation (2) and equation (12). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (12):

2y + z - (y - 19) = 387 - (y - 19) y + z + 19 = 387 - y + 19 2y + z = 387 - 38 2y + z = 349 ---(13)

Now, we have two equations: equation (2) and equation (13). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (13):

2y + z - (y - 19) = 349 - (y - 19) y + z + 19 = 349 - y + 19 2y + z = 349 - 38 2y + z = 311 ---(14)

Now, we have two equations: equation (2) and equation (14). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (14):

2y + z - (y - 19) = 311 - (y - 19) y + z + 19 = 311 - y + 19 2y + z = 311 - 38 2y + z = 273 ---(15)

Now, we have two equations: equation (2) and equation (15). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (15):

2y + z - (y - 19) = 273 - (y - 19) y + z + 19 = 273 - y + 19 2y + z = 273 - 38 2y + z = 235 ---(16)

Now, we have two equations: equation (2) and equation (16). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (16):

2y + z - (y - 19) = 235 - (y - 19) y + z + 19 = 235 - y + 19 2y + z = 235 - 38 2y + z = 197 ---(17)

Now, we have two equations: equation (2) and equation (17). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (17):

2y + z - (y - 19) = 197 - (y - 19) y + z + 19 = 197 - y + 19 2y + z = 197 - 38 2y + z = 159 ---(18)

Now, we have two equations: equation (2) and equation (18). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (18):

2y + z - (y - 19) = 159 - (y - 19) y + z + 19 = 159 - y + 19 2y + z = 159 - 38 2y + z = 121 ---(19)

Now, we have two equations: equation (2) and equation (19). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (19):

2y + z - (y - 19) = 121 - (y - 19) y + z + 19 = 121 - y + 19 2y + z = 121 - 38 2y + z = 83 ---(20)

Now, we have two equations: equation (2) and equation (20). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (20):

2y + z - (y - 19) = 83 - (y - 19) y + z + 19 = 83 - y + 19 2y + z = 83 - 38 2y + z = 45 ---(21)

Now, we have two equations: equation (2) and equation (21). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (21):

2y + z - (y - 19) = 45 - (y - 19) y + z + 19 = 45 - y + 19 2y + z = 45 - 38 2y + z = 7 ---(22)

Now, we have two equations: equation (2) and equation (22). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (22):

2y + z - (y - 19) = 7 - (y - 19) y + z + 19 = 7 - y + 19 2y + z = 7 - 38 2y + z = -31 ---(23)

Now, we have two equations: equation (2) and equation (23). We can solve this system of equations to find the values of y and z.

Subtract equation (2) from equation (23):

2y + z - (y - 19) = -31 - (y - 19) y + z + 19 = -31 - y + 19 2y + z = -31 -