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Evan and Peter have a radio show that has 2 parts. They need 4 fewer than 11 songs in the first part. In the second part, they need 5 fewer than 3 times the number of songs in the first part.

Part A

write an expression for the number of songs they need for their show.

( 11 - 4) + 3 x 11 - 4 - 5

(11 - 4) + 3 x (11 - 4) 11 - 5

(11 - 4 ) + 3 - 4 x 11 - 5

( 11 - 4 ) + 3 - 5 x ( 11 - 4 )

Part B

How many songs do they need for their show?

39 songs

31 songs

25 songs

23 songs

1 answer

Let's break it down step-by-step.

Part A

  1. First part: Evan and Peter need 4 fewer than 11 songs.

    • This can be written as: \[ 11 - 4 \]
    • That simplifies to: \[ 7 \]

  2. Second part: They need 5 fewer than 3 times the number of songs in the first part.

    • The number of songs in the first part is 7, so we need to express the second part's requirement: \[ 3 \times (11 - 4) - 5 \]
    • Replacing \(11 - 4\) with 7, we write it as: \[ 3 \times 7 - 5 \]
    • That simplifies to: \[ 21 - 5 = 16 \]

  3. Now, we combine the songs from both parts: \[ (11 - 4) + (3 \times (11 - 4) - 5) = (11 - 4) + (3 \times 7 - 5) \]

    • Simplifying: \[ 7 + 16 = 23 \]

So, the expression for the number of songs they need for their show is (11 - 4) + (3 \times (11 - 4) - 5).

Part B

Now, let's calculate the total number of songs:

  • First part: 7 songs
  • Second part: 16 songs

Combining these, we find: \[ 7 + 16 = 23 \]

Thus, the total number of songs Evan and Peter need for their show is 23 songs.

In conclusion, the answers are:

  • Part A: The expression is \((11 - 4) + (3 \times (11 - 4) - 5)\).
  • Part B: They need 23 songs in total.