SOLUTION: There are 550 people at a basketball tournament. 1/3 of the adults and 1/5 of the children wear basketball jerseys.The number of adults and children not wearing jerseys are equal.H

Click here to see ALL problems on Linear Equations And Systems Word Problems

Question 1032363: There are 550 people at a basketball tournament. 1/3 of the adults and 1/5 of the children wear basketball jerseys.The number of adults and children not wearing jerseys are equal.How many children do not wear jerseys?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let a = the number of adults.
let c = the number of children.

you get:

a + c = 550

this means the number of adults and children totals 550 in all.

1/3 * a = number of adults wearing jerseys.
1/5 * c = number of children wearing jerseys.

2/3 * a = number of adults not wearing jerseys.
4/5 * c = number of children not wearing jerseys.

you are given that the number of adults not wearing jerseys is the same as the number of children not wearing jerseys.

this means that 2/3 * a = 4/5 * c

divide both sides of the equation by (2/3) to get a = 4/5 * c / (2/3)

simplify this to get a = 6/5 * c.

in the first equation of a + c = 550, replace a with 6/5 * c to get 6/5 * c + c = 550.

simplify this to get 11/5 * c = 550.

solve for c to get c = 550 / (11/5) = 250.

since a = 6/5 * c, this means a = 500.

a + c = 550 becomes 300 + 250 = 550 which becomes 550 = 550.
this part is good.

1/3 * a = 100 adults wearing jerseys.
this means 200 adults are not wearing jerseys.

1/5 * 250 = 50 children wearing jerseys.
this means 200 children are not wearing jerseys.

the number of adults not wearing jerseys is the same as the number of children not wearing jerseys.
this part is good.

your solution is that 200 children are not wearing jerseys.

if there is any part of this that you do not understand, please let me know and i will explain it in more detail.