Chapter 4, Problem 10PT

To determine

To find: the total number of songs on both players

Answer to Problem 10PT

The required expression is $2x+37.$

Explanation of Solution

Given:

D has 37 more songs on her player than O has on his player.

Calculation:

Consider the following data:

O has some songs on his player.

D has 37 more songs on her player than O has on his player.

The objective is to write an expression in simplest form that represents the total number of songs on both players.

Assume that, O has x songs on his player.

Because D has 37 more songs on her player than O has on his player, so D has $x+37$ songs on her player.

Then the expression that represents the total number of songs on both players will be

  $\begin{array}{l}\text{= Number of songs O has on his player + Number of songs D has on her player}\hfill \\ =x+\left(x+37\right).\hfill \end{array}$

Now, simplify the last expression as follows:

  $x+\left(x+37\right)$ Write the last expression

  $=\left(x+x\right)+37$ Associative property

  $=\left(1x+1x\right)+37$ Identity property

  $=\left(1+1\right)x+37$ Distributive property

  $=2x+37.$

Simplify

Conclusion:

Therefore, the expression is $2x+37.$