Answer:
b 18 boys
Explanation:
In order to solve this problem we must create a system of equations.
Creating a system of equations
Let x = number of boys and y = # of girls
We are given that in total there are 27 children which means # of boys + # of girls = 27 so we can say x + y = 27
We are also given that there are twice as many boys as girls so we can also say x = 2y ( as # of boys = twice the number of girls )
Solving the system
Now to find the # of boys and girls we must solve the system. To do so we are going to use the substitution method.
What is the substitution method?
The substitution method is where one of your variables ( x in this case ) is defined by an expression in which you can plug in or " substitute " it into the other equation ( we can substitute x = 2y into the other equation and solve for y )
Substitute equation 2 into equation 1
Equation 1 : x + y = 27
==> plug in x = 2y
y + 2y = 27
==> combine like terms
3y = 27
==> divide both sides by 3
y = 9
So there are 9 girls in the classroom
Solving for # of boys
To solve for the number of girls we plug in the # of girls (y=9) into one of the equations and solve for x
equation : x + y = 27
==> plug in y = 9
x + 9 = 27
==> subtract 9 from both sides
x = 18
There are 18 boys in the classroom
Checking our work:
Now that we have found the possible answers we can check our work. To do so we are going to want to plug in the values of x and y into both equations and if both are true our answer is correct
Equation 1 x + y = 27
==> plug in x = 18 and y = 9
18 + 9 = 27
==> simplify
27 = 27 ✓
equation 2 x = 2y
==> plug in x = 18 and y = 9
18 = 2(9)
==> multiply 2 and 9
18 = 18 ✓
Both are correct therefore we can conclude that there are 18 boys and 9 girls.