Answer :
Answer: 25 girls came for the dance.
Step-by-step explanation:
Let x represent the number of girls that came for the ballroom dance.
Let y represent the number of boys that came for the ballroom dance.
The total number of boys and girls that came for the dance is 45. It means that
x + y = 45
He wanted to make sure girls would come, so he charged boys $5 to get in but girls only $3. The total amount paid by those who came was $175. It means that
3x + 5y = 175- - - - - - - - - - - - - -1
Substituting x = 45 - y into equation 1, it becomes
3(45 - y) + 5y = 175
135 - 3y + 5y = 175
- 3y + 5y = 175 - 135
2y = 40
y = 40/2
y = 20
x = 45 - y = 45 - 20
x = 25
By solving a system of equations, we will see that there are 20 boys and 25 girls.
How to write and solve a system of equations?
First, we need to define the variables, we will use:
- x = number of girls.
- y = number of boys.
We know that 45 tickets were sold, so:
x + y = 45
We also know that the total recaudation is $175, then:
x*$3 + y*$5 = $175
Then the system of equations is:
x + y = 45
x*$3 + y*$5 = $175
To solve this we need to isolate one of the variables in one of the equations, let's isolate x on the first one:
x = 45 - y
Now we replace this on the other equation:
(45 - y)*$3 + y*$5 = $175
And now we solve this for x:
$135 + y*$2 = $175
y = ( $175 - $135)/2 = 20
Then we have x = 45 - 20 = 25.
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904