17. Five time as many girls as boys went to the dance. The total of 120 students went to

the dance.

a. If b represents the number of boys and g represents the number of girls, use

the numbers, variables, and symbols shown below to construct a system of

equations to model this situation. Some of the numbers, variables, and

operations will be used more than once and some will not be used at all.

b

g

+

3

4

1

5

10

120

2

b. Determine the number of boys and girls went to the dance.

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