Question

John gets to play a total of 96 songs at his school dance. He wants twice as many fast songs, ​y, as ​ slow dance songs, ​x. Write a pair of equations to represent this situation and use those equations to find ​ the number of fast and slow songs John can play. Then solve for x and y.

Answer 1

Answer:

The number of fast songs is 64 and the number of slow songs is 32

Step-by-step explanation:

∵ Y represents the number of fast songs

∵ x represents the number of slow dance songs

∵ John gets to play a total of 96 songs at his school dance

→ That means the sum of x and y is 96

∴ x + y = 96 ⇒ (1)

∵ He wants twice as many fast songs, ​y, as ​ slow dance songs, ​x

→ That means y is twice x

∴ y = 2x ⇒ (2)

→ Substitute y in equation (1) by equation (2)

∵ x + 2x = 96

∴ 3x = 96

→ Divide both sides by 3 to find x

∴ $\frac{3x}{3}=\frac{96}{3}$

∴ x = 32

→ Substitute the value of x in equation (2) to find the value of y

∵ y = 2(32)

∴ y = 64

∴ The number of fast songs is 64 and the number of slow songs is 32