Question

The ninth grade class has 17 more girls than boys. There are 431 in all. How many boys are there? How many girls are there?

Answer 1

Hint: We first form an equation using the given conditions. Since the number of boys and girls we don’t know. They say that in the ninth grade class there are 17 more girls than boys, so we take the number of boys to be ‘x’. We first find the number of boys in a class then we find the number of girls.

Complete step by step solution:
Given,
Let the number of boys in the ninth grade is \['x'\] .
They also said that there are 17 more girls than boys. More means addition. Then we have,
The number of girls is \['x + 17'\] .
Also they gave the total number of students in a class is 431.
Then,
  \[x + x + 17 = 431\]
  \[2x + 17 = 431\]
Subtracting 17 on both sided we have,
  \[2x = 431 - 17\]
  \[2x = 414\]
Divide by 2 on both sides of the equation
  \[x = \dfrac{{414}}{2}\]
  \[ \Rightarrow x = 207\]
That is the number of boys in a class is 207.
The number of girls is \['x + 17'\] , substituting for ‘x’ we have,
  \[ \Rightarrow 207 + 17\]
  \[ \Rightarrow 224\]
That is the number of girls in a class is 224.
So, the correct answer is “224”.

Note: Above all we did is simple calculation. We can also check whether the obtained solution is correct or not. If we add the number of boys and the number of girls in ninth class we should get 431 in total.
We have number of boys \[ \Rightarrow 207\]
Number of girls \[ \Rightarrow 224\]
Then \[ \Rightarrow 224 + 207 = 431\] . Hence the obtained answer is correct.