tigergirl102030
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Luis spent $55 buying songs and movies at an online store that charges $1.25 for each song and 2.75 for each movie. He purchased a total of 26 songs and movies combined. Determine how many songs and how many movies Luis purchased, using either and algebraic or graphical approach.

PLEASE HELP

Respuesta :

Alright, lets get started.

Suppose Luis purchased number of songs = x

Suppose Luis purchased number of movies = y

store that charges $ 1.25 for each song and $ 2.75 for each movie.

Means his total spent will be :

[tex] 1.25 x + 2.75 y = 55 [/tex] ..................................equation (1)

He purchased a total of 26 songs and movies combined means:

[tex] x+y = 26 [/tex]

[tex] x = 26 - y [/tex]

Plugging the value of x in equation (1)

[tex] 1.25 (26-y) + 2.75 y = 55 [/tex]

[tex] 32.5 - 1.25 y + 2.75 y = 55 [/tex]

[tex] 1.5 y + 32.5 = 55 [/tex]

Subtracting 32.5 from both sides

[tex] 1.5 y + 32.5 - 32.5 = 55 - 32.5 [/tex]

[tex] 1.5 y = 22.5 [/tex]

[tex] y = 15 [/tex]

As we know, [tex] x = 26 - y [/tex]

Hence [tex] x = 26 - 15 = 11 [/tex]

It means Luis puchased 11 songs and 15 movies. : Answer

Hope it will help :)




facundo3141592

By solving a system of equations, we saw that Luis bought 15 movies and 11 songs.

How to solve a system of equations?

Let's define the variables:

  • x = number of songs bought.
  • y = number of movies bought.

We know that Luis bought a total of 26 songs and movies, then:

x + y = 26

And we know that he spent a total of $55, then:

x*$1.25 + y*$2.75 = $55

Then our system of equations is:

x + y = 26

x*$1.25 + y*$2.75 = $55

To solve this, we need to isolate one of the variables in one of the equations, I will isolate x on the first equation:

x = 26 - y

Now we can replace that on the other equation:

x*$1.25 + y*$2.75 = $55

(26 - y)*$1.25 + y*$2.75 = $55

Now we can solve this for y.

$32.50 - y*$1.25 + y*$2.75 = $55

y*$1.50 = $55 - $32.50 = $22.50

y = $22.50/$1.50 = 15

This means that Luis bought 15 movies, and:

x = 26 - y = 26 - 15 = 11

And 11 songs.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

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