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Arisa [49]
3 years ago
5

Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is a

dding 5 CDs a month to her collection. Find the number of months after which they will have the same number of CDs. show your work
Mathematics
2 answers:
timurjin [86]3 years ago
7 0

Answer:

3 months.

Step-by-step explanation:

Let x represent the number of months.

We have been given that Tom has a collection of 30 CDs and he is adding 1 CD a month to his collection.

So number of CDs in Tom's collection after x months would be: 30+x.

We are also told that Nita has a collection of 18 CDs. Nita is adding 5 CDs a month to her collection. So number of CDs in Nita's collection after x months would be: 18+5x.

To solve for number of months, when both will have same number of CDs, we will equate both expressions as:

18+5x=30+x

18+5x-x=30+x-x

18+4x=30

18-18+4x=30-18

4x=12

\frac{4x}{4}=\frac{12}{4}

x=3

Therefore, after 3 months they will have the same number of CDs.

GrogVix [38]3 years ago
6 0
30:18,
31:23
32:28
33:33
It will be three months before they have the same amount of CDs
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Answer:

La persona que ganó más dinero fue Braulio por S/.16

Step-by-step explanation:

Deje que la cantidad inicial sea Andrés X, Braulio Y y Ciro Z

Luego, dado que cada uno pierde una apuesta en el orden presentado, tenemos;

Después de la primera apuesta, tenemos;

Andrés X-Y-Z, Braulio (Y + Y), Ciro (Z + Z)

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2 (X-Y-Z), 2Y - (X-Y-Z) - 2Z, 2Z + 2Z

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En el tercero

4 (X-Y-Z), 6Y - 2X - 2Z, 4Z-2 (X-Y-Z) - (3Y - X -Z)

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4 (X-Y-Z) = 0.48 .............................. (1)

6Y - 2X - 2Z = 0.56 ...................... (2)

7Z - X - Y = 0.28 ............................ (3)

Multiplicamos las ecuaciones (2) por 2 y restamos la ecuación (1), tenemos;

12Y - 4X - 4Z - 4X + 4Y + 4Z = 0.56 * 2 - 0.48 = 0.64

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Multiplicamos las ecuaciones (2) por 7/2 y sumamos a la ecuación (3), tenemos;

21Y - 7X - 7Z + 7Z - X - Y = 7/2 * 0.56 + 0.28

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Restando la ecuación (4) de la ecuación (5) tenemos;

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De la ecuación (5), tenemos;

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De la ecuación (3), tenemos;

7Z - X - Y = 7Z - 0.72 - 0.4 = 0.28

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Por lo tanto tienen inicialmente

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Y₁ = 0.4

Z₁ = 0.2

Después de jugar tienen;

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Y₂ = 0.56

Z₂ = 0.28

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Ciro 0.28 - 0.2 = 0.08

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