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Question 1165717: Rachel and Mari is a student athlete, they have played for Manila Meet, Palarong
Pambansa and represented our school in UAAP. So far, Rachel has won 24 out of 40
matches.
a. Write a rational equation for the given
b. How many matches will Rachel have to win in a row to improve her winning percentage
to 75 %?
c. How many matches will Rachel have to win in a row to improve her winning percentage
to 90%?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! so far rachel has won 24 out of 40.
her winning percentage is 24 / 40 * 100 = 60%.
let y equal the percent of matches she has won.
let x = the number of matches she has to to win.
when x = 40, the number of wins is 24 for a percentage of wins of 24/40 = .6 * 100 = 60%.
our equation will be y = x / (x + 16) * 100.
y represents the percent of games won.
x represents the number of games won
x + 16 represents the number of games played.
x/(x+16) represents the ratio of games won.
x/(x+16) represents the percent of games won.
since rachel has to win every additional match she plays, the number of wins and the number of games played increments by 1 every time x increments by 1.
when y = 60, the equation becomes:
60 = x / (x + 16) * 100
multiply both sides of this equation by (x + 16) to get:
60 * (x + 16) = 100 * x
factor the left side of this equation to get:
60 * x + 60 * 16 = 100 * x
subtract 60 * x from both sides of this equation to get:
60 * 16 = 100 * x - 60 * x
simplify to get:
960 = 40 * x
solve for x to get:
x = 960 / 40 = 24.
when x = 24, she has won 24 games out of a total of 40 games for a winning percentage of 24/40 * 100 = 60%.
when y = 75, the equation becomes:
75 = x / (x + 16) * 100
multiply both sides of this equation by (x + 16) to get:
75 * (x + 16) = 100 * x
simplify to get:
75 * x + 16 * 75 = 100 * x
subtract 75 * x from both sides of the equation and simplify to get:
1200 = 25 * x
solve for x to get:
x = 1200 / 25 = 48
when x = 48, she has won 48 games out of a total of 64 games for a winning percentage of 48/64 * 100 = 75%.
when y = 90, the equation becomes:
90 = x / (x + 16) * 100
multiply both sides of this equation by (x + 16) to get:
90 * (x + 16) = 100 * x
simplify to get:
90 * x + 1440 = 100 * x
subtract 90 * x from both sides of the equation to get:
1440 = 10 * x
solve for x to get:
x = 144
when x = 144, she has won 144 games out of 160 for a winning percentage of 144 / 160 * 100 = 90%.
the equation can be graphed.
it looks like this:
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