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Readme [11.4K]
3 years ago
8

Helppp meee plssss

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
3 0

Answer:

a)200x+250y \leq 44000\\ x+y \leq 150,\ where\ x\ is\ the\ number\ of\ children,\ and\ y\ is\ the\ number\ of\ adults.\\ c)The\ number\ of\ children\ and\ adults\ respectively\ maybe\ (20,100),\\ (100,20),(40,40),(80,60).

Step-by-step explanation:

We\ are\ given\ that,\\Cost\ of\ the\ Ticket\ To\ the\ Play\ for\ Adults= 250\ php\\Cost\ of\ the\ Ticket\ To\ the\ Play\ for\ Children=200\ php\\Maximum\ number\ of\ Adults\ and\ Children\ permitted\ to\ watch\ the\ play=150\ heads\\Maximum\ amount\ to\ be\ collected\ after\ the\ sales=44,000\ php

a)Let\ the\ number\ of\ Children\ who\ attended\ the\ play\ be\ x.\\Let\ the\ number\ of\ Adults\ who\ attended\ the\ play\ be\ y.\\Hence,\\(Total\ Cost\ of\ the\ ticket\ for\ Children)+(Total\ Cost\ of\ the\ ticket\ for\\ Adults) \leq 44,000.\\(No.\ of\ Children\ who\ attended\ the\ play)+(No.\ of\ Adults\ who\ attended\ the\ play) \leq 150.\\Hence,\\200x+250y \leq 44000\\x+y \leq 150Hence,\\We've\ found\ the\ inequalities\ that\ best\ represent\ our\ conditions, and\ paired\\ them\ into\ a\ system\ of\ inequalities.

b) [Kindly\ refer\ the\ graph\ attachment]\\\\We've\ drawn\ the\ graph\ fixing\ the\ scale\ of\ 1\ unit\ to\ be\ 20\ heads (Adults\ or\ Children).\\The\ red\ slope\ and\ the\ red\ area\ shaded\ below\ it,\ represent\ Inequality\ 1.\\The\ blue\ slope\ and\ the\ blue\ area\ shaded\ below\ it,\ represent\ Inequality\ 2.\\As\ we\ already\ know\ that,\\The\ overlapped\ region\ contains\ the\ solutions\ to\ the\ system\ of\ Inequalities.

c)Considering\ any\ four\ points\ on\ the\ overlapped\ region,\ would\ work\ great.\\Also,\\We\ need\ to\ be\ a\ bit\ cautious\ here\ and\ consider\ solutions\ only\ from\ the\\ First\ Quadrant,\ as\ the\ physical\ quantity-Counting\ Numbers\ can\\ only\ be\ Whole\ Numbers.

Now,\\Lets\ consider\ points\ (20,100), (100,20),(40,40),(80,60).\\Lets\ verify\ for\ each\ of\ them\ separately:\\

I]Substituting\ x=20,\ y=100\ in\ Inequality\ 1:\\200x+250y \leq 44000\\200*20+250*100 \leq 44000\\4000+25000 \leq 44000\\29000 \leq 44000\\This\ is\ TRUE.\\\\Substituting\ x=20,\ y=100\ in\ Inequality\ 2:\\x+y \leq 150\\20+100 \leq 150\\120 \leq 150\\This\ is\ TRUE\ too.

II]\ Substituting\ x=100,\ y=20\ in\ Inequality\ 1:\\200x+250y \leq 44000\\200*100+250*20 \leq 44000\\20000+5000 \leq 44000\\25000 \leq 44000\\This\ is\ TRUE.\\\\Substituting\ x=100,\ y=20\ in\ Inequality\ 2:\\x+y \leq 150\\100+20 \leq 150\\120 \leq 150\\This\ is\ TRUE\ too.

III]\ Substituting\ x=40,\ y=40\ in\ Inequality\ 1:\\200x+250y \leq 44000\\200*40+250*40 \leq 44000\\8000+10000 \leq 44000\\18000 \leq 44000\\This\ is\ TRUE.\\\\Substituting\ x=40,\ y=40\ in\ Inequality\ 2:\\x+y \leq 150\\40+40 \leq 150\\80 \leq 150\\This\ is\ TRUE\ too.

IV]\ Substituting\ x=80,\ y=60\ in\ Inequality\ 1:\\200x+250y \leq 44000\\200*80+250*60 \leq 44000\\16000+15000 \leq 44000\\31000 \leq 44000\\This\ is\ TRUE.\\\\Substituting\ x=80,\ y=60\ in\ Inequality\ 2:\\x+y \leq 150\\80+60 \leq 150\\140 \leq 150\\This\ is\ TRUE\ too.

Hence,\ Verified.

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