Question

В мозаике 160 кусочков смальты светлого цвета.Это в 4 раза больше,чем кусочков тёмного цвета.Акусочков золотистого цвета в 10 раз больше,чем кусочков светлых и тёных вместе.сколько кусочков золотистого цвета в мозаике?

Answer 1

160:4=40(тёмный цвет)
160+40=200(тёмные и светлые цвета)
200:10=20(золотистый цвет)

Answer 2

Solution:

To solve this problem, we can use a system of equations to represent the given information and then solve for the number of pieces of the gold color.

Let's denote: - x as the number of pieces of light-colored enamel. - y as the number of pieces of dark-colored enamel. - z as the number of pieces of gold-colored enamel.

We are given the following information: 1. There are 160 pieces of enamel in total, with 4 times as many light-colored pieces as dark-colored pieces: - x + y + z = 160 - x = 4y

2. The number of gold-colored pieces is 10 times the sum of the light and dark-colored pieces: - z = 10(x + y)

Solution Steps:

1. Substitute the value of x from the second equation into the first equation to express y in terms of z. 2. Substitute the expression for y into the equation for the total number of pieces to solve for z.

Calculations:

Substituting x = 4y into the equation x + y + z = 160 gives: - 4y + y + z = 160 - 5y + z = 160

Substituting z = 10(x + y) into the equation x + y + z = 160 gives: - x + y + 10(x + y) = 160 - x + y + 10x + 10y = 160 - 11x + 11y = 160 - x + y = 160 / 11

Substituting x = 4y into the equation x + y = 160 / 11 gives: - 4y + y = 160 / 11 - 5y = 160 / 11 - y = 32 / 11

Substituting y = 32 / 11 into the equation x = 4y gives: - x = 4 * (32 / 11) - x = 128 / 11

Substituting x and y into the equation z = 10(x + y) gives: - z = 10(128 / 11 + 32 / 11) - z = 10(160 / 11) - z = 1600 / 11 - z ≈ 145.45

Answer:

So, there are approximately 145 pieces of gold-colored enamel in the mosaic.