Reviewer Labas mga Math Wizard, sagutin mo may 20 pesos load! Globe lang haha

[PHC Diver]

First to answer show your solutions.
Legit? yes legit.
Topic: Diophantine Equations
Prize: 20 Autoload Max (Will increase by 5 pesos every hour, limit at 100)
PS: Wag mo na hanapin sa google hahaha

A traveler is selling three items.
Potion = 50
Boots = 100
Cloak = 250

He sold a total of 67 pcs of the items and earned exactly 10,000.
How many of each is sold?

 

[Slaughter]

21×50 = 1050 -- Potion
17×100 = 1700 -- Boots
29 × 250 = 7250 -- Cloak

 

[PHC Diver]

láρág number

 

[PHC - plokplok]

x = Potion
y = Boots
z = Cloak

Since si Cloak ang pinakamahal, pwede syang laruin like z = x+2y , z=5x , z=3x+y.
Pinakamadali is hanapin yung lowest possible value ni z. Which we can do by letting the cheapest item to be zero.

x + y + z = 67
50x + 100y + 250z = 10,000

Let x be 0
100(y + z = 67)

---

100y + 100z = 6700
100y + 250z = 10,000

---

(-150z = -3300)/-150
z=22

---

y + 22 = 67
y= 67 - 22

---

y=45

Set#1(x=0,y=45,z=22)

Since nakuha na yung lowest value ni 22, add lang ng 1 sa kanya to find other possible sets.

Let z be 23, tapos ihiwalay na sya sa equation
67-23=
23x250=5,750
10,000-5750=4250

100(x + y = 44)
50x + 100y = 4250

---

100x + 100y = 4400
50x + 100y = 4250

---

(50x = 150)/50
x=3

3+y=44
y=41

Set#2(x=3,y=41,z=23)

---

Let z be 24(add uli ng 1)
67-24=43

---

10000-(24x250)=4000

---

100(x+y=43)
50x+100y=4000

---

100x+100y=4300
50x+100y=4000

---

(50x=300)/50
x=6

---

6+y=43
y=37

Set#3(x=6,y=37,z=24)

Observing the 3 first sets, habang tumataas ng isa si z, tumataas nang tatlo si x at bumababa naman ng apat si y.

z+1=(x+3)+(y-4)


So continuing that until the lowest positive number of y, the possible are number of each items sold are as follows.

---

---

---

Final Answer:
x is Potion
y is Boots
z is Cloak

Set#1(x=0,y=45,z=22)
Set#2(x=3,y=41,z=23)
Set#3(x=6,y=37,z=24)
Set#4(x=9,y=33,z=25)
Set#5(x=12,y=29,z=26)
Set#6(x=15,y=25,z=27)
Set#7(x=18,y=21,z=28)
Set#8(x=21,y=17,z=29)
Set#9(x=24,y=13,z=30)
Set#10(x=27,y=9,z=31)
Set#11(x=30,y=5,z=32)
Set#12(x=33,y=1,z=33)


Meron pa yan, kaso nga lang since items yan di pwede mag negative. Pwede din naman lets say nanakaw so bawas sa sales yun. Pero di ko na nilagay bwisit na ako eh

 

[PHC - plokplok]

[XX='PHC Diver, c: 552369, m: 729323'][/XX]
Hala sya, awit sayo tignan mo sagot ko.

PHC Diver ,akala ko ba with solution?

Ano yan, kung ako prof mo zero points yan sakin.

 

[PHC - plokplok]

[XX='PHC Diver, c: 552369, m: 729323'][/XX] Hayop ka pinahirapan mo ako hahaha.

K A I T O pasok ka dito. Check mo nga yung sagot ko.

 

[PHC Diver]

haha kinonsider mo lahat , divisible by 50 lahat kaya pwede may 0 sa potion haha, dali láρág number, dun palang may sagot na hehe

 

[PHC - plokplok]

With solution sabi mo malamang ganyan. Di naman tatanggaping solution yung random guess until makuha yung sasaktong 10k.

Di considered a valid solution yun. Kahit hindi sa math competition kahit sa school lang di yun coconsider.

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[PHC Diver]

Sorna sir haha , well, congratulations narin haha

 

[PHC - plokplok]

[XX='PHC Diver, c: 552436, m: 729323'][/XX]
Nareceive ko na yung load, salamat haha.

Ok lang yun, nawarm up ako mag math pa naman ako sa module.