Question

Масса груши и апельсина 550г масса груши и яблока 530г.Найди массу каждого фрукта если масса эти трёх фруктов 830г.Записать задачу двумя способами и с пояснением .

Answer 1

1) 830-530=300(гр)-апельсин
2) 830-550=280(гр)-яблоко
3) 830-(300+280)=150(гр)-груша
Ответ: 300, 280, 150 гр.

Answer 2

Problem Statement:

Масса груши и апельсина составляет 550 г, а масса груши и яблока составляет 530 г. Найдите массу каждого фрукта, если общая масса трех фруктов составляет 830 г.

Solution 1:

Let's assume the mass of the pear is x grams and the mass of the orange is y grams.

According to the problem statement, the mass of the pear and the orange is 550 grams, so we can write the equation: x + y = 550 [[1]]

Similarly, the mass of the pear and the apple is 530 grams, so we can write another equation: x + z = 530 [[2]]

We need to find the mass of each fruit, so we have three unknowns: x, y, and z.

To solve this system of equations, we can subtract equation [[2]] from equation [[1]] to eliminate the variable x: (x + y) - (x + z) = 550 - 530 y - z = 20 [[3]]

Now we have two equations with two unknowns (y and z). We can solve this system of equations to find the values of y and z.

Let's assume the mass of the apple is z grams.

From equation [[3]], we know that y - z = 20. We can rearrange this equation to solve for y: y = z + 20 [[4]]

We also know that the total mass of the three fruits is 830 grams, so we can write another equation: x + y + z = 830 [[5]]

Now we have three equations with three unknowns (x, y, and z). We can substitute equation [[4]] into equation [[5]] to eliminate the variable y: x + (z + 20) + z = 830 2z + x + 20 = 830 2z + x = 810 [[6]]

We can now solve equations [[3]] and [[6]] simultaneously to find the values of y and z.

By substituting equation [[6]] into equation [[3]], we get: (810 - x) - z = 20 810 - x - z = 20 -z = 20 - 810 + x -z = -790 + x z = 790 - x [[7]]

Substituting equation [[7]] into equation [[6]], we get: 2(790 - x) + x = 810 1580 - 2x + x = 810 1580 - x = 810 -x = 810 - 1580 -x = -770 x = 770 [[8]]

Now that we have the value of x, we can substitute it back into equation [[7]] to find the value of z: z = 790 - x z = 790 - 770 z = 20 [[9]]

Finally, we can substitute the values of x and z into equation [[4]] to find the value of y: y = z + 20 y = 20 + 20 y = 40 [[10]]

Therefore, the mass of the pear is 770 grams, the mass of the orange is 40 grams, and the mass of the apple is 20 grams.

Solution 2:

Let's assume the mass of the pear is x grams, the mass of the orange is y grams, and the mass of the apple is z grams.

According to the problem statement, the mass of the pear and the orange is 550 grams, so we can write the equation: x + y = 550 [[1]]

Similarly, the mass of the pear and the apple is 530 grams, so we can write another equation: x + z = 530 [[2]]

We need to find the mass of each fruit, so we have three unknowns: x, y, and z.

To solve this system of equations, we can subtract equation [[2]] from equation [[1]] to eliminate the variable x: (x + y) - (x + z) = 550 - 530 y - z = 20 [[3]]

Now we have two equations with two unknowns (y and z). We can solve this system of equations to find the values of y and z.

From equation [[3]], we know that y - z = 20. We can rearrange this equation to solve for y: y = z + 20 [[4]]

We also know that the total mass of the three fruits is 830 grams, so we can write another equation: x + y + z = 830 [[5]]

Now we have three equations with three unknowns (x, y, and z). We can substitute equation [[4]] into equation [[5]] to eliminate the variable y: x + (z + 20) + z = 830 2z + x + 20 = 830 2z + x = 810 [[6]]

We can now solve equations [[3]] and [[6]] simultaneously to find the values of y and z.

By substituting equation [[6]] into equation [[3]], we get: (810 - x) - z = 20 810 - x - z = 20 -z = 20 - 810 + x -z = -790 + x z = 790 - x [[7]]

Substituting equation [[7]] into equation [[6]], we get: 2(790 - x) + x = 810 1580 - 2x + x = 810 1580 - x = 810 -x = 810 - 1580 -x = -770 x = 770 [[8]]

Now that we have the value of x, we can substitute it back into equation [[7]] to find the value of z: z = 790 - x z = 790 - 770 z = 20 [[9]]

Finally, we can substitute the values of x and z into equation [[4]] to find the value of y: y = z + 20 y = 20 + 20 y = 40 [[10]]

Therefore, the mass of the pear is 770 grams, the mass of the orange is 40 grams, and the mass of the apple is 20 grams.

Please note that the solution is the same for both methods, but the steps are presented differently.