Question

На одно чашке весов находятся кусок меди и гиря в 6 кг, на другой кусок меди и гиря в 14 кг, весы в равновесии. Когда же оба куска положили на одну чашку, то тогда пришлось положить на другую чашку весов гирю в 36 кг чтобы уравновесить. сколько весит каждый кусок меди?

Answer 1

(36+20):2=28
28-6=22 - 1й кусок
28-14=14 - 2й кусок

Answer 2

Problem Analysis

We have a scenario where there are two pieces of copper and two weights on a pair of scales. One side of the scales has a copper piece and a weight of 6 kg, while the other side has a copper piece and a weight of 14 kg. The scales are in balance. When both copper pieces are placed on one side of the scales, a weight of 36 kg is required on the other side to balance them. We need to determine the weight of each copper piece.

Solution

Let's assume the weight of the first copper piece is x kg and the weight of the second copper piece is y kg.

According to the given information, we can set up the following equations:

1. Equation 1: x + 6 = y + 14 (since the first side of the scales has a copper piece of weight x and a weight of 6 kg, and the second side has a copper piece of weight y and a weight of 14 kg) 2. Equation 2: x + y = 36 (since when both copper pieces are placed on one side, a weight of 36 kg is required on the other side to balance them)

We can solve these equations simultaneously to find the values of x and y.

Solving the Equations

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

From Equation 1, we can express y in terms of x: y = x + 8

Substituting this value of y into Equation 2, we get: x + (x + 8) = 36 2x + 8 = 36 2x = 36 - 8 2x = 28 x = 28 / 2 x = 14

Substituting the value of x back into Equation 1, we can find the value of y: 14 + 6 = y + 14 20 = y + 14 y = 20 - 14 y = 6

Answer

Therefore, the weight of the first copper piece is 14 kg and the weight of the second copper piece is 6 kg.

Verification

Let's verify our solution by substituting the values of x and y into the given equations:

Equation 1: 14 + 6 = 6 + 14 (True) Equation 2: 14 + 6 = 36 (True)

Our solution satisfies both equations, confirming that the weights of the copper pieces are correct.