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19 May, 19:22

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.

+1
Answers (1)
  1. 19 May, 20:15
    0
    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
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