Answered

Jonathan uploaded some original songs and also some pictures. Alissa uploaded four times as many songs, but only uploaded twice as many pictures. Jonathan uploaded 11 items while Alissa uploaded 24. How many songs did Jonathan upload?



Answer :

X is the number of songs and Y the number of pics
1:X+y=11
2:4x+2y=24

1: x=11-y

Lets replace x in 2:
4(11-y) +2y=24
44-4y+2y=24
44-24= 4y-2y
20= 2y
Y=20/2
Y=10

Lets replace y in 1
X+10=11
X=11-10
X=1

Jonathan uploaded 1 song
The correct answer is:
Jonathan uploaded 1 song.

Explanation:
Let s be the number of songs Jonathan uploaded, and p be the number of pictures he uploaded.
Together he uploaded 11 items, which gives us
s+p=11.
 Alissa uploaded 4 times as many songs, or 4s, and twice as many pictures, or 2p.
Together she uploaded 24 items, which gives us
4s+2p=24.

To solve this system of equations I will use substitution.
First, isolate a variable in our first equation, s+p=11.
We can isolate s by subtracting p from each side:
s+p-p=11-p;
s=11-p.

Now substitute this into the second equation:
4(11-p)+2p=24.

Use the distributive property:
4*11-4*p+2p=24;
44-4p+2p=24.

Combine like terms:
44-2p=24.

Subtract 44 from both sides:
44-2p-44=24-44;
-2p=-20.

 Divide both sides by -2:
-2p/-2=-20/-2;
p=10.

Jonathan uploaded 10 pictures.
Using this in the first equation, s+10=11; subtract 10 from both sides:
s+10-10=11-10;
s=1.
Jonathan uploaded 1 song.