Chapter 1.4, Problem 48IP

Solution

(a)

What expression should Denzel evaluate in order to find the total number of boys.

  $x+y+z;17+28+13$

Given:

Club	Boys	Girls
Chess	17	19
Drama	28	23
Music	13	21

Explanation:

In order to write what expression should Denzel evaluate in order to find the total number of boys, let the number of boys which play chess is x, let the number of boys which play drama is y, and then let the number of boys which play music is z , to find the total number of boys adding the number of boys in chess, the number of boys in drama, and the number of boys in music, so the expression is as shown below:

  $x+y+z$

So, the expression is $x+y+z$

(b)

Explain how can you can use property of numbers to make the expression easier to evaluate using mental math.

Concept Used:

Associative property of Addition

  $a+\left(b+c\right)=\left(a+b\right)+c$

In order to explain how can we use the property of numbers to make the expression easier to evaluate using mental math, to evaluate the expression by using associative property of addition:

  $a+\left(b+c\right)=\left(a+b\right)+c$

Now putting the values a=17, b=28, c=13 ,

  $\begin{array}{l}17+\left(28+13\right)=\left(17+28\right)+13\\ 17+41=45+13\\ 58=58\end{array}$

This is true because the left hand side and the right hand side are equal.