Answer:
Part a) System of equations:
g = 5 b
b + g = 120
Part b) There were 20 boys, and 100 girls at the dance.
Step-by-step explanation:
Part a)
We start by writing a mathematical expression associated with he two given statements:
1) "Five times as many girls as boys" using "g" to represent the number of girls, and "b" for the number of boys:
g = 5 b
2) a "Total of 120 students" ...
This means that the addition of boys "b" and girls "g" should render 12:
b + g = 120
Part b)
Solve for the number of boys and girls by first replacing (substituting) "g" with "5 b" in the second equation, solving for "b":
b + 5 b = 120
6 b = 120
b = 120/6
b = 20
and now that we know the number of boys, finding the number of girls "g" using the first equation:
g = 5 (20)
g = 100
