Answer:
Step-by-step explanation:
Let the total number of votes to choose a color = x
Number of votes for blue = ![\frac{5}{8}\times x](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B8%7D%5Ctimes%20x)
Remaining votes = x - ![\frac{5}{8}\times x](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B8%7D%5Ctimes%20x)
= ![\frac{8x-5x}{8}\times x](https://tex.z-dn.net/?f=%5Cfrac%7B8x-5x%7D%7B8%7D%5Ctimes%20x)
= ![\frac{3}{8}\times x](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B8%7D%5Ctimes%20x)
Votes for green = ![\frac{5}{9}\times (\text{Remaining votes})}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B9%7D%5Ctimes%20%28%5Ctext%7BRemaining%20votes%7D%29%7D)
= ![\frac{5}{9}\times \frac{3x}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B9%7D%5Ctimes%20%5Cfrac%7B3x%7D%7B8%7D)
= ![\frac{5}{24}\times x](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B24%7D%5Ctimes%20x)
Finally remaining votes = ![\frac{3x}{8}-\frac{5x}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B8%7D-%5Cfrac%7B5x%7D%7B24%7D)
= ![\frac{9x-5x}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B9x-5x%7D%7B24%7D)
= ![\frac{4x}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%7D%7B24%7D)
= ![\frac{x}{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B6%7D)
Since these votes are for red therefore,
= 48
x = 48×6
= 288
a) Votes for blue are ![\frac{5x}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B5x%7D%7B8%7D)
Therefore, exact number for blue votes = ![\frac{5\times 288}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Ctimes%20288%7D%7B8%7D)
= 5×36
= 180
b). Votes for green = ![\frac{5x}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B5x%7D%7B24%7D)
= ![\frac{5\times 288}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Ctimes%20288%7D%7B24%7D)
= 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 = ![\frac{7}{10}\times 180](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B10%7D%5Ctimes%20180)
= 7×18
= 126
Since total votes made = 288
Therefore, half of the votes made = ![\frac{288}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B288%7D%7B2%7D)
= 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.