Question

Riverside Elementary School is holding a school-wide election to choose a school color. Five-eighths of the votes were for blue, 5/9 of the remaining votes were for green, and the remaining 48 votes were for red.

a. How many votes were for blue?
b. How many votes were for green?
c. If every student got one vote, but there were 25 students absent on the day of the vote, how many students are there at Riverside Elementary School?
d. Seven-tenths of the votes for blue were made by girls. Did girls who voted for blue make up more than or less than half of all votes? Support your reasoning with a picture.
e. How many girls voted for blue?

Answer 1

Explanation:

Let the total number of votes to choose a color = x

Number of votes for blue =
`(5)/(8)* x`

Remaining votes = x -
`(5)/(8)* x`

=
`(8x-5x)/(8)* x`

=
`(3)/(8)* x`

Votes for green =
`(5)/(9)* (\text{Remaining votes})}`

=
`(5)/(9)* (3x)/(8)`

=
`(5)/(24)* x`

Finally remaining votes =
`(3x)/(8)-(5x)/(24)`

=
`(9x-5x)/(24)`

=
`(4x)/(24)`

=
`(x)/(6)`

Since these votes are for red therefore,

`(x)/(6)` = 48

x = 48×6

= 288

a) Votes for blue are
`(5x)/(8)`

Therefore, exact number for blue votes =
`(5* 288)/(8)`

= 5×36

= 180

b). Votes for green =
`(5x)/(24)`

=
`(5* 288)/(24)`

= 60

c). Since 25 students were absent on that day of the vote, number of students at Riverside Elementary School = 288 + 25

= 313

d). Since seven tenths of the votes for blue were made by the girls.

Therefore, number of girls voted for blue =
`(7)/(10)* 180`

= 7×18

= 126

Since total votes made = 288

Therefore, half of the votes made =
`(288)/(2)`

= 144

Now it's clear that number of votes made by girls is less than half of all the votes.

e). 126 girls voted for blue.