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hammer [34]
3 years ago
13

A web store offers two versions of a popular song. the size of the standard version is 2.5 megabytes. the size of the high-quali

ty version is 4.6 megabytes. yesterday there were 1230 downloads of the song, for a total download size of 4797 megabytes. how many downloads of the standard version were there?
Mathematics
1 answer:
Komok [63]3 years ago
3 0
---------------------------------------------------
Define x and y :
---------------------------------------------------
Let x the number of 2.5M downloads.
Let y the number of 4.6M downloads.

---------------------------------------------------
Construct Equations :
--------------------------------------------------
There was a total of 1230 downloads.
⇒ x + y = 1230

Total downloaded size was 4797M.
⇒2.5x + 4.6y = 4797

---------------------------------------------------
Find x and y :
---------------------------------------------------
x + y = 1230 -------------------- (1)
2.5x + 4.6y = 4797 ------------ (2)

---------------------------------------------------
From equation 1 :
---------------------------------------------------
x + y = 1230
x = 1230 - y                               // Take away y on both sides

---------------------------------------------------
Sub x = 1230 - y into equation 2 :
---------------------------------------------------
2.5 (1230 - y) + 4.6y = 4797      // Sub x = 1230 
3075 - 2.5y + 4.6y = 4797         // Apply distributive property
3075 + 2.1y = 4797                   // Combine like terms
2.1y = 1722                               // Take away 3075 from both sides
y = 820                                      // Divide by 2.1 on both sides

---------------------------------------------------
Sub y = 820 into equation 1 to find x :
---------------------------------------------------
x + y = 1230   
x + 820 = 1230                        // Sub y = 820
x = 410                                     // Take away 820 from both sides

---------------------------------------------------
Find the number of each type of downloads :
---------------------------------------------------
Number of 2.5M downloads = x = 410
Number of 4.6M downloads = y = 820 

-------------------------------------------------------------------------------------
Answer: There were 410 downloads for the standard version.
-------------------------------------------------------------------------------------

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y=\frac{32}{15} =2\frac{2}{15} \ units

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It cost $5 for his brother's ticket.

Step-by-step explanation:

Let,

Micheal's ticket price= x

His brother ticket price = y

According to given statement;

x+y=12    Eqn 1

y = x-2    Eqn 2

Putting value of y from Eqn 2 in Eqn 1

x+(x-2)=12\\x+x-2=12\\2x=12+2\\2x=14\\

Dividing both sides by 2;

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Putting x=7 in Eqn 2

y=7-2\\y=5

It cost $5 for his brother's ticket.

Keywords: linear equation, substitution method

Learn more about linear equations at:

  • brainly.com/question/2747595
  • brainly.com/question/2750627

#LearnwithBrainly

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IrinaK [193]

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Step-by-step explanation:

* Lets talk about dilation

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- It can become larger or smaller, but the shape of the

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- The scale factor, measures how much larger or smaller  

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- If the scale factor between 0 and 1, then the image will be smaller

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* Now lets solve the problem

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- The image K'L'M'N' of figure KLMN after dilation about the origin

  has four vertices:

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- From (1) and (2)

# (3 , -3) ⇒ (6 , -6)

# (3 , 4) ⇒ (6 , 8)

# (5 , 4) ⇒ (10 , 8)

# (5 , -3) ⇒ (10 , -6)

- Each point in KLMN multiplied by 2

∴ The scale of dilation is 2

∴ The rule of dilation centered at the origin is (x , y) → (2x , 2y)

3 0
3 years ago
Read 2 more answers
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