Question 236176: Write a system of two equations in two unknowns for each
problem. Solve each system by the method of your choice.
One-half of the boys and one-third of the
girls of Freemont High attended the homecoming game,
whereas one-third of the boys and one-half of the
girls attended the homecoming dance. If there were
570 students at the game and 580 at the dance, then how
many students are there at Freemont High?
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! X/2+Y/3=570 MULTIPLY BY 2
X/3+Y/2=580 MULTIPLY BY -3 & ADD
X+2Y/3=1140
-X-3Y/2=-1,740
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2Y/3-3Y/2=-600
(2*2Y-3Y*3)/2*3=-600
(4Y-9Y)/6=-600
-5Y=-600*5
-5=-3,600
Y=-3,600/-5
Y=720 ANS. NUMBER OF GIRLS.
X/2+720/3=570
X/2+240=570
X/2=570-240
X/2=330
X=330*2
X=660 ANS. NUMBER OF BOYS.
PROOF:
660/3+720/2=580
220+360=580
580=580
BOYS = GIRLS
660+720=1,380 TOTAL NUMBER OF STUDENTS.
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