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Eğitmen, Ali-Veli, Berat-Sema, baba-çocuk ve anne-kız gibi farklı yaş problemlerini çözerek, iki bilinmeyenli problemleri tek bilinmeyene düşürme tekniklerini göstermektedir.","Eğitmen, yaş farkının değişmediği, yaşların oranı bire yaklaştığı ve yaş ortalamasının kişi yaşı gibi ilerlediği gibi temel bilgileri vurgulamakta ve yaş problemlerinin aslında çok zor olmadığını, çözümlerinin genellikle basit olduğunu belirtmektedir."]},"endTime":940,"title":"Yaş Problemleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Yaş Problemlerinin Temel Bilgileri","list":{"type":"unordered","items":["Yaş problemleri, öğrencilerin en sevdikleri problem türlerinden biridir.","Yaş farkı hiçbir zaman değişmez, örneğin ben hoca'dan beş yaş büyüksem, kaç sene geçerse geçsin beş yaş büyük olmaya devam edeceğim.","Yaşların oranı zamanla bire yaklaşır, örneğin 20/21, 40/41, 55/56 gibi oranlar bire daha yakın 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yaşından sekiz fazla olduğunda, yedi yıl sonra yaşları toplamı 44 olacak şekilde problem çözülebilir.","Baba 42, çocuğu 8 yaşında olduğunda, kaç yıl sonra babanın yaşı çocuğun yaşının iki katı olur sorusu için, x değişkeni kullanılarak 26 yıl sonra bulunur.","Anne kız probleminde, anne kızının yaşının sekiz katı olduğunda, kız büyüyüp annenin bugünkü yaşının yarısına geldiğinde yaşları toplamı 60 olacak şekilde, kız 4 yaşında, anne 32 yaşında bulunur."]},"beginTime":255,"endTime":403,"href":"/video/preview/10896488958037886176?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=255&ask_summarization=1"},{"index":3,"title":"Daha Karmaşık Yaş Problemleri","list":{"type":"unordered","items":["Baba ile oğlunun yaşları toplamı 36 olduğunda, oğlunun şu anki yaşının üç katına geldiğinde yaşları oranı 7/3 olduğunda, babanın bugünkü yaşı 30 olarak hesaplanır.","Üç çocuk ve annenin yaş probleminde, çocuklar üçer yıl arayla doğmuş olduğunda, en küçük çocuk doğduğunda anne ve çocukların yaşları hesaplanabilir."]},"beginTime":403,"endTime":521,"href":"/video/preview/10896488958037886176?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=403&ask_summarization=1"},{"index":4,"title":"Yaş Problemleri Çözümü","list":{"type":"unordered","items":["Bir soruda, çocukların yaşları toplamının dört katından dokuz çıkarıldığında 35 olduğu belirtiliyor ve x=13 olarak bulunuyor.","Ortanca çocuğun şu anki yaşı 13+3=16 olarak hesaplanıyor.","Bir başka soruda, babanın yaşı iki kızının yaşları farkının yedi katı ve 15 yıl sonra babanın yaşı kızların yaşları farkının on katı olarak veriliyor."]},"beginTime":527,"endTime":570,"href":"/video/preview/10896488958037886176?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=527&ask_summarization=1"},{"index":5,"title":"Yaş Problemlerinde Dikkat Edilmesi Gerekenler","list":{"type":"unordered","items":["Yaş problemlerinde, zaman geçtikçe yaşlar artar ancak yaş farkı değişmez.","İki kızın yaşları toplamı 7 olarak bulunuyor.","Erhan ve Selim'in yaşları oranı 7/2 olarak veriliyor ve Selim'in Erhan'ın yaşındayken 5x kadar sene önce olduğu belirtiliyor."]},"beginTime":570,"endTime":672,"href":"/video/preview/10896488958037886176?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=570&ask_summarization=1"},{"index":6,"title":"İki Bilinmeyenli ve Tek Bilinmeyenli Çözüm Yöntemleri","list":{"type":"unordered","items":["Yaş problemlerini iki bilinmeyenli veya tek bilinmeyenli olarak çözebilirsiniz, ancak tek bilinmeyenli çözümde mantık veya işaret hataları yapılabilir.","İki kardeşin yaşları toplamı 27 ve küçük kardeş büyük kardeşin yaşına geldiğinde yaşları toplamı 49 olacak.","İki bilinmeyenli çözümde, yaş farkı 11 olarak bulunuyor ve büyük kardeşin yaşı 19 olarak hesaplanıyor."]},"beginTime":672,"endTime":768,"href":"/video/preview/10896488958037886176?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=672&ask_summarization=1"},{"index":7,"title":"Aile Yaş Ortalaması Problemi","list":{"type":"unordered","items":["Beş kişilik bir ailenin yaş ortalaması 21 ve üç sene sonra 24 olacak.","Üç sene sonra bir çocuk daha doğduğunda, yaş ortalaması 24 olacak.","Küçük çocuk 2 yaşına geldiğinde, yaş ortalaması tekrar 21 olacak ve bu durum küçük çocuk doğduktan bir yıl sonra gerçekleşecek."]},"beginTime":768,"endTime":849,"href":"/video/preview/10896488958037886176?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=768&ask_summarization=1"},{"index":8,"title":"Aile Yaş Farkı Problemi","list":{"type":"unordered","items":["Bir ailede baba ile annenin yaşları farkı, çocukların yaşları farkının 3 katı olarak veriliyor.","a ve b değerleri için 3a=4b denklemi bulunuyor.","Baba ve anne için en düşük değerler 4 ve 3 olarak verildiğinde, baba en az 43 yaşında olabilir."]},"beginTime":849,"endTime":937,"href":"/video/preview/10896488958037886176?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=849&ask_summarization=1"}],"linkTemplate":"/video/preview/10896488958037886176?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Yaş Problemleri | Matematik | Hocalara 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Problemleri / Şenol HOCA Merhaba arkadaşlar! YKS 2020 programında beklediğiniz Problemler Serisi geldi! Serinin bu videosunda Yaş Problemleri soru çözümlerini bulabilirsin.","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3291710/a62cfd067b38aaf5db95b954e771d14f/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/nKIsOAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"7","reqid":"1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=videoid:15800119936026249742","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin yaş problemlerini anlattığı kapsamlı bir eğitim içeriğidir. Öğretmen, öğrencilere hitap ederek adım adım problemleri çözerek konuyu açıklamaktadır.","Videoda yaş problemlerinin çözüm yöntemleri detaylı olarak ele alınmaktadır. Öğretmen, yaş problemlerinin aslında sayı problemleri olduğunu vurgulayarak, tablo yöntemi, grafik okuma ve mantık kullanarak problemleri çözme tekniklerini göstermektedir. Video, kolaydan zora doğru çeşitli örnekler üzerinden ilerlemekte ve ÖSYM sınavlarında çıkabilecek karmaşık yaş problemlerinin çözüm tekniklerini içermektedir.","Öğretmen ayrıca yaş problemleri ile sayı basamakları arasındaki ilişkiyi de açıklamakta, \"23a + b = 72\" gibi denklemleri çözerek a ve b değerlerini bulma yöntemlerini göstermektedir. Video sonunda öğrencilere \"çıtır çerez problemler\" ve ÖSYM formatındaki problemleri çözmeleri tavsiye edilmektedir."]},"endTime":2056,"title":"Yaş Problemleri Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Yaş Problemlerinin Temel Kavramları","list":{"type":"unordered","items":["Yaş problemleri aslında sayı problemleridir ve yeni bir problem türü olarak düşünülmemelidir.","İki kişi arasındaki yaş farkı hiç değişmez, çünkü her iki kişi de aynı miktarda büyür.","Yaş problemlerinde tablo yapmak temel çözüm yöntemidir."]},"beginTime":9,"endTime":60,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=9&ask_summarization=1"},{"index":1,"title":"Yaş Problemlerinin Çözüm Yöntemi","list":{"type":"unordered","items":["Yaş problemlerinde tablo yaparak şimdiki yaşları ve sonraki yaşları belirlemek gerekir.","Aradan geçen süre her iki kişinin yaşlarında da aynı miktarda artar.","Yaşlar toplamı, aradan geçen yıl ile kişi sayısının çarpımı kadar artar."]},"beginTime":60,"endTime":96,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=60&ask_summarization=1"},{"index":2,"title":"Örnek Problemler","list":{"type":"unordered","items":["Bir çocukla annesinin yaşları oranı 2:5 olduğunda, çocuk annesinin yaşına geldiğinde anne 56 yaşında olacağına göre anne ile çocuk arasındaki yaş farkı 21'dir.","Destan doğduğunda abisi Destanın şimdiki yaşının iki katından dört fazlası yaştaydı ve bugün ikisinin yaşları toplamı 36 olduğuna göre Destan doğduğunda abisi 20 yaşında idi.","Mehtap, Cengiz ve Tanju'nun yaşları toplamı 72'dir ve dört yıl sonra bu üç arkadaşın yaşları toplamı Mehtabın yaşının dört katı olacaktır. Mehtap şu an 17 yaşında olduğuna göre Cengiz ve Tanju'nun bugünkü yaşları toplamı 55'tir."]},"beginTime":96,"endTime":464,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=96&ask_summarization=1"},{"index":3,"title":"Grafik Okuma ve Yaş Problemi","list":{"type":"unordered","items":["Dört arkadaşın doğum yılları verilmiş: Rümesa 1998, Hanife 2000, Sezgin 2002, Yasemin 2006 ve hocanın doğum yılı 1326 olarak belirtilmiş.","Grafikte X yılında arkadaşların yaşları toplamı 58, Y yılında ise 74 olarak gösterilmiş.","Yaşlar toplamı 16 artmış, bu da her arkadaşın 4 yaş arttığı anlamına gelmiş ve X ve Y yılları arasında 4 yıl fark olduğu bulunmuş."]},"beginTime":468,"endTime":622,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=468&ask_summarization=1"},{"index":4,"title":"Gezi Grubu Yaş Problemi","list":{"type":"unordered","items":["Bir gezi grubundaki yolcuların yaşları toplamı rehberin yaşının 5 katından 3 fazladır.","Üç yıl sonra aynı gezi grubundaki yolcuların yaşları toplamı aynı rehberin yaşının 7 katı olacak.","Bu süre içinde rehberin yaşı 1/10 oranında artmış ve gezi grubunda hiçbir yolcu katılmadığı gibi ayrılan da olmamıştır.","Rehberin yaşı 30, gezi grubunda toplam 26 yolcu olduğu hesaplanmıştır."]},"beginTime":622,"endTime":877,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=622&ask_summarization=1"},{"index":5,"title":"Aritmetik Ortalama Problemi","list":{"type":"unordered","items":["Bir grupta 15, 20 ve 25 yaşında kaç kişinin olduğu gösterilmiştir: 15 yaşında 20 kişi, 20 yaşında 15 kişi, 25 yaşında 10 kişi.","Toplam yaş toplamı 850 olarak hesaplanmıştır.","Kişi sayısı 45 olduğundan, yaş ortalaması 18,88 olarak bulunmuştur."]},"beginTime":877,"endTime":976,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=877&ask_summarization=1"},{"index":6,"title":"Yaş Ortalaması Problemi","list":{"type":"unordered","items":["Grupta 45 kişi bulunuyor ve yaş ortalaması 18,80 olarak verilmiş.","20 yaşında 5 kişi gruba katılırsa, grubun yaş ortalaması artar çünkü 20 yaşında insanlar ortalamanın üstünde gelir.","25 yaşında 5 kişi ayrılırsa, grubun yaş ortalaması düşer çünkü yaşlı olanlar grubun ortalamasını yukarı çekiyor."]},"beginTime":980,"endTime":1101,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=980&ask_summarization=1"},{"index":7,"title":"Aile Yaşları Problemi","list":{"type":"unordered","items":["Hilal, abisinin ve ablasının yaşları toplamı a iken doğmuş.","Hilal'in yaşı a+3 olduğunda, abisinin ve ablasının yaşları toplamı a+5+b olur.","Denklem kurularak b=2/3a ilişkisi bulunur."]},"beginTime":1101,"endTime":1251,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=1101&ask_summarization=1"},{"index":8,"title":"Üç Kardeşin Yaşları Problemi","list":{"type":"unordered","items":["Ayşe'nin yaşı 150 derecelik açıya denk gelen bir daire dilimi oluşturmuş, Beril ve Ceylin aynı yaştadır.","Üç kardeşin yaşları toplamı 75'ten az olduğuna göre, Ayşe en fazla 30 yaşında olabilir.","Yaşlar 10, 7 ve 7'nin katları şeklinde orantılıdır ve Ayşe'nin yaşı 10 katı olmalıdır."]},"beginTime":1256,"endTime":1426,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=1256&ask_summarization=1"},{"index":9,"title":"Dört Kardeşin Yaşları Problemi","list":{"type":"unordered","items":["Dört kardeşin yaşları toplamı 120'dir ve her kardeşin yaşı diğerlerinin yaşları toplamının belirli bir oranıdır.","Birinci kardeşin yaşı diğerlerinin yaşları toplamının yarısıdır, ikinci kardeşin yaşı üçte biri, üçüncü kardeşin yaşı dörtte biridir.","Dördüncü kardeşin yaşı 26 yaşında olarak bulunmuştur."]},"beginTime":1426,"endTime":1608,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=1426&ask_summarization=1"},{"index":10,"title":"Öğrenme Tavsiyeleri","list":{"type":"unordered","items":["Öğretmen, öğrencilerin soruları çözerken aktif olmalarını ve yazarak çalışmalarını tavsiye etmektedir.","Aktif çalışmanın öğrenmenin daha kalıcı olmasını sağladığını vurgulamaktadır.","Bol soru çözmek ve çözemediği soruların çözümlerini öğrenmek öğrenmenin temelidir."]},"beginTime":1608,"endTime":1652,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=1608&ask_summarization=1"},{"index":11,"title":"İki Basamaklı Sayı Problemi","list":{"type":"unordered","items":["Ayşe'nin yaşı 11a, Fatma'nın yaşı 10a+b olarak hesaplanmıştır.","İki kardeşin bir yıl sonraki yaşları toplamı 72 olduğuna göre, yeni yaşları 12a+b ve 11a+2b olarak bulunmuştur.","Yeni yaşları toplamı 23a+3b=72 denklemine eşitlenerek çözüm devam etmektedir."]},"beginTime":1652,"endTime":1754,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=1652&ask_summarization=1"},{"index":12,"title":"Yaş Problemleri ve Sayı Basamakları","list":{"type":"unordered","items":["Yaş problemi sayı basamakları ile entegre olmuş ve ÖSYM'nin en sevdiği konulardan biridir.","Bu tür sorular algılaması zor olabilir ancak algıladıktan sonra çözümü basit olur.","Örnek soruda 23a + b = 72 eşitliği verilmiş ve a ve b birer rakamdır."]},"beginTime":1757,"endTime":1795,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=1757&ask_summarization=1"},{"index":13,"title":"Örnek Sorunun Çözümü","list":{"type":"unordered","items":["a'ya 1, 2 ve 3 değerleri denendiğinde sadece a=3 ve b=1 değerleri eşitliği sağlar.","a=3 ve b=1 olduğunda, a-b=2 olur ve iki yıl önceki yaşları toplamı 60'dır.","Şu anki yaşları 33 ve 31 olan kişilerin iki yıl önceki yaşları toplamı 60'dır."]},"beginTime":1795,"endTime":1934,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=1795&ask_summarization=1"},{"index":14,"title":"Dairesel Grafik Problemi","list":{"type":"unordered","items":["Bir toplatıya üç yaş grubundan insanlar katılmış ve yaş gruplarına göre oluşan dairesel grafik verilmiştir.","30 yaşındaki insanlar 90 derecelik açıya, 40 yaşındaki insanlar 150 derecelik açıya karşılık gelmektedir.","Dereceleri sadeleştirip 4, 3 ve 5 ile orantılı hale getirerek kişi sayılarını bulup, katılımcıların yaşları ortalaması 38,5 olduğuna göre taralı bölgeyi oluşturan gruptaki kişi sayısını hesaplamak gerekir."]},"beginTime":1934,"endTime":2028,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=1934&ask_summarization=1"},{"index":15,"title":"Ödev ve Kapanış","list":{"type":"unordered","items":["Öğrencilere çıtır çerez problemleri ve ÖSYM formatta problemler soru bankasından veya sınav ikisinden soru çözmeleri ödevi verilmiştir.","Matematik soru çözerken öğrenilir."]},"beginTime":2028,"endTime":2045,"href":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=2028&ask_summarization=1"}],"linkTemplate":"/video/preview/15800119936026249742?parent-reqid=1769521903973696-4557120573200722072-balancer-l7leveler-kubr-yp-vla-149-BAL&text=JuniorDaProblem&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Yaş problemleri / şenol 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