SOLUTION: Kim is thinking of 2 numbers. The quotient is 4 and the difference is 27. What are the 2 numbers? Kylie and Ellie played basketball. Kylie scored half as many points as Ellie.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Kim is thinking of 2 numbers. The quotient is 4 and the difference is 27. What are the 2 numbers? Kylie and Ellie played basketball. Kylie scored half as many points as Ellie.      Log On


   

Question 163449: Kim is thinking of 2 numbers. The quotient is 4 and the difference is 27. What are the 2 numbers?

Kylie and Ellie played basketball. Kylie scored half as many points as Ellie.
Together they scored 27 points. How many did each player score?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Kim is thinking of 2 numbers. The quotient is 4 and the difference is 27. What are the 2 numbers?
ANSWER:
x=1stnumber
x%2B1=2nd+number
1st condition: x%2F%28x%2B1%29=4, cross multiply
4%28x%2B1%29=x
4x%2B4=x
4x-x=-4 -----> 3x=-4 ---> cross%283%29x%2Fcross%283%29=-4%2F3
x=-4%2F3
Go back to the condition to check,
%28-4%2F3%29%2F%28%28-4%2F3%29%2B1%29=4
%28-4%2F3%29%2F%28highlight%28%28-4%2B3%29%2F3%29%29=4, get LCD
%28-4%2F3%29%283%2F-1%29=4 ---> %28-4%2Fcross%283%29%29%28cross%283%29%2F-1%29=4
%28-4%29%28-1%29=4
4=4, oks!
Therefore, %28-4%2F3%29=1stNumber; -1%2F3=2ndNumber see above highlighted
Kylie and Ellie played basketball. Kylie scored half as many points as Ellie.
Together they scored 27 points. How many did each player score?
ANSWER:
x=score of Ellie
%281%2F2%29x=score of Kylie
Total score=27pts
Then, x%2B%281%2F2%29x=27, EQN 1
%282x%2Bx%29%2F2=27, get LCD
3x=54, cross multiply
cross%283%29x%2Fcross%283%29=cross%2854%2918%2Fcross%283%29
x=18pts ---------------> score of Ellie
%281%2F2%2918=9pts ----------> score of Kylie
Check via EQN 1,
18%2B9=27pts, oks!
Thank you,
Jojo