Chapter 6.5, Problem 23HP

To determine

To formulate a system of equations relating to the given condition and solving the system of equations.

Answer to Problem 23HP

  $\begin{array}{l}x+y=48\\ x=10+y\end{array}$

Explanation of Solution

Given:

Formulate a system of equations that represent a situation in your school.

Concept used:

The system of equations formulated are solved using substitution method.

Consider the question:

There are 48 students in a class. The number of boys is 10 more than the number of girls. How many girls are there in the class?

Let x be the number of boys and y be the number of girls.

Given that the total students are 48.

  $\Rightarrow x+y=48$

Also, the number of boys is 10 more than the number of girls.

  $\Rightarrow x=10+y$

Substitute the above equation in $x+y=48$ ,

  $\begin{array}{l}\Rightarrow (10+y)+y=48\\ \Rightarrow 10+2y=48\\ \Rightarrow 2y=38\\ \Rightarrow y=19\end{array}$

Substitute in $x=10+y,$

  $\begin{array}{l}\Rightarrow x=10+19\\ \Rightarrow x=29\end{array}$

Conclusion:

Therefore, the number of boys in the class is 29 and the number of girls in the class is 19.