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Sagot :
Let's solve the problem by finding three different ways to decompose the total number of mosaics needed, using the expressions given in the table.
First, let's sum up the total number of mosaics needed:
Piso 1: 874 mosaicos
Piso 2: 3241 mosaicos
Planta baja: 655 mosaicos
Total de mosaicos necesarios:
[tex]\[ 874 + 3241 + 655 = 4770 \][/tex]
Now, we will find three different decompositions for the total of 4770 mosaicos using the expressions provided in the table.
### Descomposition 1
The first decomposition can be represented by the following expressions:
[tex]\[ 250 \times 8 + 100 \][/tex]
[tex]\[ 500 \times 4 + 100 \][/tex]
[tex]\[ 209 \times 10 + 10 \][/tex]
These calculations result in:
[tex]\[ 250 \times 8 + 100 = 2000 + 100 = 2100 \][/tex]
[tex]\[ 500 \times 4 + 100 = 2000 + 100 = 2100 \][/tex]
[tex]\[ 209 \times 10 + 10 = 2090 + 10 = 2100 \][/tex]
So, the total for this decomposition is:
[tex]\[ 2100 + 2100 + 2100 = 6300 \][/tex]
### Descomposition 2
The second decomposition can be represented by the following expressions:
[tex]\[ 250 \times 100 + 45 \][/tex]
[tex]\[ 50 \times 20 + 45 \][/tex]
[tex]\[ 500 \times 2 + 45 \][/tex]
These calculations result in:
[tex]\[ 250 \times 100 + 45 = 25000 + 45 = 25045 \][/tex]
[tex]\[ 50 \times 20 + 45 = 1000 + 45 = 1045 \][/tex]
[tex]\[ 500 \times 2 + 45 = 1000 + 45 = 1045 \][/tex]
So, the total for this decomposition is:
[tex]\[ 25045 + 1045 + 1045 = 27135 \][/tex]
### Descomposition 3
The third decomposition can be represented by the following expressions:
[tex]\[ 10 \times 100 + 50 \][/tex]
[tex]\[ 8 \times 100 + 50 \][/tex]
[tex]\[ 40 \times 20 + 50 \][/tex]
These calculations result in:
[tex]\[ 10 \times 100 + 50 = 1000 + 50 = 1050 \][/tex]
[tex]\[ 8 \times 100 + 50 = 800 + 50 = 850 \][/tex]
[tex]\[ 40 \times 20 + 50 = 800 + 50 = 850 \][/tex]
So, the total for this decomposition is:
[tex]\[ 1050 + 850 + 850 = 2750 \][/tex]
### Summary
In summary, we have the total number of mosaics needed as:
[tex]\[ 4770 \][/tex]
And three different decompositions of the total number of mosaics are:
1. \( 6300 \)
2. \( 27135 \)
3. \( 2750 \)
These decompositions show various ways to reach numbers close to the total number of mosaics using the provided expressions in the table.
First, let's sum up the total number of mosaics needed:
Piso 1: 874 mosaicos
Piso 2: 3241 mosaicos
Planta baja: 655 mosaicos
Total de mosaicos necesarios:
[tex]\[ 874 + 3241 + 655 = 4770 \][/tex]
Now, we will find three different decompositions for the total of 4770 mosaicos using the expressions provided in the table.
### Descomposition 1
The first decomposition can be represented by the following expressions:
[tex]\[ 250 \times 8 + 100 \][/tex]
[tex]\[ 500 \times 4 + 100 \][/tex]
[tex]\[ 209 \times 10 + 10 \][/tex]
These calculations result in:
[tex]\[ 250 \times 8 + 100 = 2000 + 100 = 2100 \][/tex]
[tex]\[ 500 \times 4 + 100 = 2000 + 100 = 2100 \][/tex]
[tex]\[ 209 \times 10 + 10 = 2090 + 10 = 2100 \][/tex]
So, the total for this decomposition is:
[tex]\[ 2100 + 2100 + 2100 = 6300 \][/tex]
### Descomposition 2
The second decomposition can be represented by the following expressions:
[tex]\[ 250 \times 100 + 45 \][/tex]
[tex]\[ 50 \times 20 + 45 \][/tex]
[tex]\[ 500 \times 2 + 45 \][/tex]
These calculations result in:
[tex]\[ 250 \times 100 + 45 = 25000 + 45 = 25045 \][/tex]
[tex]\[ 50 \times 20 + 45 = 1000 + 45 = 1045 \][/tex]
[tex]\[ 500 \times 2 + 45 = 1000 + 45 = 1045 \][/tex]
So, the total for this decomposition is:
[tex]\[ 25045 + 1045 + 1045 = 27135 \][/tex]
### Descomposition 3
The third decomposition can be represented by the following expressions:
[tex]\[ 10 \times 100 + 50 \][/tex]
[tex]\[ 8 \times 100 + 50 \][/tex]
[tex]\[ 40 \times 20 + 50 \][/tex]
These calculations result in:
[tex]\[ 10 \times 100 + 50 = 1000 + 50 = 1050 \][/tex]
[tex]\[ 8 \times 100 + 50 = 800 + 50 = 850 \][/tex]
[tex]\[ 40 \times 20 + 50 = 800 + 50 = 850 \][/tex]
So, the total for this decomposition is:
[tex]\[ 1050 + 850 + 850 = 2750 \][/tex]
### Summary
In summary, we have the total number of mosaics needed as:
[tex]\[ 4770 \][/tex]
And three different decompositions of the total number of mosaics are:
1. \( 6300 \)
2. \( 27135 \)
3. \( 2750 \)
These decompositions show various ways to reach numbers close to the total number of mosaics using the provided expressions in the table.
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