Chapter 6.2, Problem 37PPE

To determine

Equation to model the situation.

Answer to Problem 37PPE

The equation is $x+y=350$ and girls are 20 more than boys.

Explanation of Solution

Given data:

The total number of students are 350 students.

The ratio of boys to girls is $33:37$

Calculation:

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

total number of students:

  $x+y=350$

Ratio of boys to girls :

  $\begin{array}{l}\frac{x}{y}=\frac{33}{37}\\ y=\frac{37}{33}x\end{array}$

Number of boys:

  $\begin{array}{l}x+y=350\\ \frac{37}{33}x+x=350\\ \frac{70}{33}x=350\\ x=165\end{array}$

Number of girls:

  $\begin{array}{l}=350-165\\ =185\end{array}$

So girls are 20 more than boys.

• The $y=\frac{37}{33}x$ will be solve first as it will be easier to substitute in the other equation and finding solution will easier. If we will solve the $x+y=350$ than it will become difficult as after substituting it in other equation than values become complicated.
• Step-1:Making the equation of given data

  $x+y=350$

  $y=\frac{37}{33}x$

Step-2:substituting the value of x from $y=\frac{37}{33}x$ in the $x+y=350$

Step-3:Find the value x and y.

Step-4:Difference of x and y gives number of girls more than boys.

Conclusion:

The equation is $x+y=350$ and girls are 20 more than boys.