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Word problems: kahani se equation tak

Short mein jawab

Word problem ko equation se hal karne ke liye anjaan cheez ko ek akshar do, baaton ko equation mein likho, dono taraf ek hi step karke solve karo, aur poochhe gaye sawaal ka jawab do. Jaise 25p + 50 = 500 se p = 18 log Madhubanti ki party mein aa sakte hain, to wo 13 dost bula sakti hai.

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Har word problem ke chaar steps

Har baar ye chaar steps follow karo, to word problems aasaan ho jaate hain:

  1. Unknown ka naam rakho: ek akshar chuno aur batao wo kis cheez ke liye hai.
  2. Baatein likho: problem ki har baat usi akshar se likho.
  3. Equation banao: jo do raashiyan barabar hain unse equation likho aur solve karo.
  4. Sawaal ka jawab do: jo poocha gaya wahi batao, aur kahani mein check karo.

Tiles ka pattern

Ranjana square tiles se T ki shape banaati hai: Step 1 mein 4 tiles, Step 2 mein 7 aur Step 3 mein 10. Step k pe upar ki line mein beech ki tile ke dono taraf k tiles hain, aur neeche k tiles ka danda latakta hai, to kul hain k + k + k + 1 = 3k + 1. Kya wo theek 100 tiles laga sakti hai? 3k + 1 = 100 solve karo: 3k = 99, to k = 33. Step 33 mein theek 100 tiles lagti hain.

Ranjana ka T shape tile pattern: Step 1 se 4 tak 4, 7, 10 aur 13 tiles, to Step k mein 3k + 1
Ranjana ki tiles

Paise: ek party aur do bachat karne waali

Madhubanti party ke snacks pe ₹500 kharch kar sakti hai. Ek plate ₹25 ki hai, aur dukaan ghar tak pahunchaane ke ₹50 leti hai. Agar kul p log aayein, to kharcha 25p + 50 hai, isliye 25p + 50 = 500. Phir 25p = 450 aur p = 18. Uske parivaar mein 5 log hain, to wo 13 dost bula sakti hai. Doosra tareeka: doston ki ginti f maano; tab 25(f + 5) = 450, to f + 5 = 18 aur f = 13. Dono tareekon se ek hi jawab.

₹500 ki patti: ₹25 ki 18 plates, 5 parivaar ke liye aur 13 doston ke liye, aur ₹50 delivery
Madhubanti ki party

Jahnavi ke paas shuru mein ₹4,000 hain aur wo har mahine ₹650 bachaati hai, jabki Sunita ke paas ₹5,050 hain aur wo har mahine ₹500 bachaati hai. m mahine baad unke paas 4000 + 650m aur 5050 + 500m honge. Inhe barabar rakho to 150m = 1050, to m = 7. Check: 7 mahine baad dono ke paas ₹8,550 hain.

Bachat ki do seedhi lines jo mahina 7 pe kaatti hain, jab dono ke paas ₹8,550 hain
7 mahine baad barabar bachat

Sankhyaon ke jaadu

Riyaz, Akash se ek sankhya sochne, usme se 3 ghataane, 4 se guna karne aur 8 jodne ko kehta hai; Akash batata hai 24. Sankhya ko x maano, to steps se aata hai x − 3, phir 4x − 12, phir 4x − 4. To 4x − 4 = 24, 4x = 28 aur x = 7. Ye niyam har jawab pe chalta hai: shuru ki sankhya hai jawab ÷ 4, plus 1. Ek akshar us jaadu ko bhi samjhaata hai jisme har koi, chahe koi bhi sankhya soche, 8 pe pahunchta hai.

Riyaz ki trick aur hamesha 8 waala jaadu, har step x se likha hua
x se sankhyaon ke jaadu

Do unknown, ek akshar

Ramesh aur Suresh ke paas milkar 60 kanche hain, aur Ramesh ke paas Suresh se 30 zyaada hain. Lagta hai do unknown hain, par ek akshar kaafi hai: agar Suresh ke paas y hain, to Ramesh ke paas y + 30. Phir y + (y + 30) = 60, to 2y = 30 aur y = 15. Suresh ke paas 15 kanche hain aur Ramesh ke paas 45. Yahi tarkeeb is sawaal ko bhi hal karti hai ki do sankhyaon ka jod 76 hai aur ek doosri ki teen guna hai: x + 3x = 76 se x = 19, to sankhyayein 19 aur 57 hain.

Bar model: Suresh ke paas y kanche, Ramesh ke paas y aur 30 zyaada, aur dono ke paas milkar 60
Ramesh aur Suresh

Jawab se equations banaana

Hum ulta bhi chal sakte hain: solution se shuru karke equations banao. y = 5 se, dono taraf 2 jodo to y + 2 = 7, 3 se guna karo to 3y + 6 = 21, aur 6 ghataao to 3y = 15. Har nayi equation ka solution wahi hai, kyunki dono taraf ek hi step kiya gaya. Chain mein waapas upar jaane ke liye ulte steps ulte kram mein lagte hain.

y = 5 solution waali do equation chains, book ke steps se neeche aur ulte steps se waapas upar
Equation chains

Equation ko kahani ki tarah bhi padh sakte hain. 100x + 75 = 250 ka matlab ho sakta hai ₹x ki 100 pencil aur ₹75 delivery, kul bill ₹250, to ek pencil ₹1.75 ki hai.

Ye kyun zaroori hai

In steps se tiles, paison ya kanchon ka sawaal ek chhoti si equation ban jaata hai. Solve karne ka abhyaas equations kaise solve karein mein karo, aur dekho Bhaskaracharya ne aise sawaal kaise poochhe bijaganita: pracheen Bharat mein algebra mein. Textbook ke sawaalon ke jawab Part 2 Chapter 7 ke NCERT solutions mein hain; poore Part 2 Chapter 7 ke notes dekho.

Practice karo

  1. Ranjana ke Step k mein 3k + 1 tiles lagti hain. Theek 100 tiles kis step mein lagengi?

    1. (a) Step 30
    2. (b) Step 33
    3. (c) Step 34
    4. (d) Step 99
    Jawab dekho

    Jawab: (b) Step 33

  2. Taxi ka kiraaya ₹800 roz aur har km ke ₹20 hai. Bill ₹2200 hai. Kitne km chale?

    1. (a) 60
    2. (b) 70
    3. (c) 80
    4. (d) 110
    Jawab dekho

    Jawab: (b) 70

  3. Do sankhyaon ka jod 76 hai, aur ek doosri ki teen guna hai. Chhoti sankhya hai:

    1. (a) 19
    2. (b) 25
    3. (c) 38
    4. (d) 57
    Jawab dekho

    Jawab: (a) 19

  4. Koi sankhya socho, use dugna karo, 10 jodo, aadha karo, sochi hui sankhya ghataao aur 3 jodo. Jawab hamesha 8 kyun aata hai?

    Jawab dekho

    Jawab: Sankhya ko x kaho. Steps se milta hai 2x, phir 2x + 10, phir x + 5, phir x ghataane pe 5, aur 3 jodne pe 8. x kat jaata hai, isliye jawab chuni hui sankhya pe nirbhar nahi karta.

  5. Do aisi equations likho jinka solution u = 6 ho.

    Jawab dekho

    Jawab: Jaise u + 4 = 10 aur 3u − 5 = 13. u = 6 rakhne pe 6 + 4 = 10 aur 18 − 5 = 13, to dono sahi hain.

Students ke sawal

Word problem ko equation mein kaise badlein?

Problem padho aur tay karo ki kya anjaan hai. Use ek akshar do, jaise logon ki ginti ke liye p. Baaki raashiyan usi akshar se likho, jaise p plates ki keemat 25p. Phir wo baat likho ki do raashiyan barabar hain, yahan 25p + 50 = 500, aur use solve karo.

Kya word problem bina equation ke bhi hal ho sakta hai?

Aksar haan. Party waale sawaal mein Fatima ne bas ₹500 mein se delivery ka kharcha ghataaya aur 25 se bhaag diya. Equation yahi kaam ek tay tareeke se karti hai, jo tab kaam aata hai jab sankhyayein badi hon ya unknown dono taraf ho.

Diye gaye solution se equations kaise banayein?

Jawab se shuru karo, jaise y = 5, aur dono taraf baar baar ek hi operation karo: 2 jodo to y + 2 = 7, 3 se guna karo to 3y + 6 = 21, aur aise hi aage. Aisi chain ki har equation ka solution ek hi hota hai.

Koi sawal atak gaya?

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