Question

Nina has 3 times as many songs on her music player as Thomas, and Matthew has 5 times as many songs on his music player as Thomas. Altogether, they have 243 songs on their music players. How many songs does each person have?

A) Nina has 81 songs, Thomas has 27 songs, and Matthew has 135 songs.
B) Nina has 72 songs, Thomas has 24 songs, and Matthew has 120 songs.
C) Nina has 60 songs, Thomas has 20 songs, and Matthew has 100 songs.
D) Nina has 90 songs, Thomas has 30 songs, and Matthew has 150 songs.

Answer 1

To solve this problem, we can use a system of equations. Thomas has 27 songs, Nina has 81 songs, and Matthew has 135 songs.

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let's assume Thomas has x number of songs on his music player.

According to the problem, Nina has 3 times as many songs as Thomas, so Nina has 3x songs.

Matthew has 5 times as many songs as Thomas, so Matthew has 5x songs.

Altogether, they have 243 songs, so we can write the equation: x + 3x + 5x = 243.

Combining like terms, we have 9x = 243.

Dividing both sides by 9, we find x = 27.

Therefore, Thomas has 27 songs, Nina has 3 times that number, which is 3 * 27 = 81 songs, and Matthew has 5 times that number, which is 5 * 27 = 135 songs.

So the answer is option A) Nina has 81 songs, Thomas has 27 songs, and Matthew has 135 songs.