{"id":1478,"date":"2025-12-31T10:00:53","date_gmt":"2025-12-31T09:00:53","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1478"},"modified":"2025-12-31T10:00:57","modified_gmt":"2025-12-31T09:00:57","slug":"zadanie-151","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1478","title":{"rendered":"Zadanie 151"},"content":{"rendered":"\n<p><strong>zadanie 35. zbi\u00f3r zada\u0144 CKE (zadanie otwarte) <\/strong><\/p>\n\n\n\n<p>Pani Joanna postanowi\u0142a systematycznie oszcz\u0119dza\u0107 i co miesi\u0105c na swoje subkonto odk\u0142ada\u0107 pewn\u0105 sum\u0119 pieni\u0119dzy. Pierwszego czerwca 2020 roku wp\u0142aci\u0142a 300 z\u0142otych. Pierwszego dnia ka\u017cdego miesi\u0105ca wp\u0142aca o 25 z\u0142 wi\u0119cej ni\u017c w miesi\u0105cu poprzednim.<\/p>\n\n\n\n<p><strong>zadanie<\/strong> <strong>35.1. (1pkt) <\/strong>Oblicz kwot\u0119, jak\u0105 pani Joanna wp\u0142aci\u0142a na subkonto pierwszego czerwca 2022 roku.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-odp\" id=\"odp_69e22d9053c62\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22d9053c62\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c odpowied\u017a\n        <\/button>\n\n        <div class=\"premium-content-odp\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \nPrawid\u0142owa odpowied\u017a to: 875 z\u0142.\n        <\/div>\n    <\/div>\n    \n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-wyjasnienie\" id=\"wyjasnienie_69e22d9053c6e\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22d9053c6e\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c wyja\u015bnienie\n        <\/button>\n\n        <div class=\"premium-content-wyjasnienie\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \n<h2>Wyja\u015bnienie<\/h2>\n\n<p>Pani Joanna odk\u0142ada co miesi\u0105c pieni\u0105dze, tworz\u0105c ci\u0105g arytmetyczny wp\u0142at.<\/p>\n\n<h3>Dane z zadania<\/h3>\n<ul>\n  <li>Pierwsza wp\u0142ata (czerwiec 2020): <strong>300 z\u0142<\/strong><\/li>\n  <li>Ka\u017cdego miesi\u0105ca wp\u0142aca o <strong>25 z\u0142<\/strong> wi\u0119cej<\/li>\n<\/ul>\n\n<h3>Krok 1: Ustalenie numeru wyrazu<\/h3>\n<p>Od czerwca 2020 do czerwca 2022 mija dok\u0142adnie 24 miesi\u0105ce, wi\u0119c szukamy <strong>24. wp\u0142aty<\/strong>.<\/p>\n\n<h3>Krok 2: Wz\u00f3r na n-ty wyraz ci\u0105gu arytmetycznego<\/h3>\n<p><code>a\u2099 = a\u2081 + (n \u2212 1)r<\/code><\/p>\n\n<p>Podstawiamy dane:<\/p>\n\n<p>\na\u2082\u2084 = 300 + 23 \u00b7 25<br>\na\u2082\u2084 = 300 + 575 = <strong>875 z\u0142<\/strong>\n<\/p>\n\n<h3>Wniosek<\/h3>\n<p>Pani Joanna wp\u0142aci\u0142a pierwszego czerwca 2022 roku <strong>875 z\u0142<\/strong>.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n<p><strong>zadanie 35.2 (2pkt)<\/strong> Oblicz, o ile wi\u0119ksz\u0105 kwot\u0119 ni\u017c w miesi\u0105cu poprzednim pani Joanna Powinna odk\u0142ada\u0107, aby pierwszego czerwca 2025 roku (uwzgl\u0119dniaj\u0105c r\u00f3wnie\u017c wp\u0142at\u0119 w tym dniu) na subkoncie by\u0142a kwota 76860 z\u0142otych.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-odp\" id=\"odp_69e22d9053c71\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22d9053c71\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c odpowied\u017a\n        <\/button>\n\n        <div class=\"premium-content-odp\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \nPrawid\u0142owa odpowied\u017a to: o 7 z\u0142.\n        <\/div>\n    <\/div>\n    \n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-wyjasnienie\" id=\"wyjasnienie_69e22d9053c74\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22d9053c74\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c wyja\u015bnienie\n        <\/button>\n\n        <div class=\"premium-content-wyjasnienie\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \n<h2>Wyja\u015bnienie<\/h2>\n\n<p>Pani Joanna odk\u0142ada pieni\u0105dze w spos\u00f3b tworz\u0105cy ci\u0105g arytmetyczny. Wiemy, \u017ce:<\/p>\n\n<ul>\n  <li>pierwsza wp\u0142ata (czerwiec 2020): <strong>300 z\u0142<\/strong>,<\/li>\n  <li>liczba miesi\u0119cy od czerwca 2020 do czerwca 2025: <strong>61 wp\u0142at<\/strong>,<\/li>\n  <li>suma wszystkich wp\u0142at ma wynie\u015b\u0107 <strong>76 860 z\u0142<\/strong>.<\/li>\n<\/ul>\n\n<h3>Krok 1: Wz\u00f3r na sum\u0119 ci\u0105gu arytmetycznego<\/h3>\n\n<p>\nS\u2099 = (a\u2081 + a\u2099) \u00b7 n \/ 2  \n<\/p>\n\n<p>Podstawiamy dane:<\/p>\n\n<p>\n76 860 = (300 + a\u2086\u2081) \u00b7 61 \/ 2\n<\/p>\n\n<h3>Krok 2: Obliczenie a\u2086\u2081<\/h3>\n\n<p>\n(300 + a\u2086\u2081) \u00b7 61 = 153 720  \n<\/p>\n\n<p>Dzielimy przez 61:<\/p>\n\n<p>\n300 + a\u2086\u2081 = 2520  \n<\/p>\n\n<p>\na\u2086\u2081 = 2220\n<\/p>\n\n<h3>Krok 3: Wyznaczenie r\u00f3\u017cnicy r<\/h3>\n\n<p>Wz\u00f3r na n-ty wyraz ci\u0105gu:<\/p>\n\n<p>\na\u2086\u2081 = 300 + 60r\n<\/p>\n\n<p>Podstawiamy:<\/p>\n\n<p>\n300 + 60r = 2220  \n<\/p>\n\n<p>\n60r = 1920  \n<\/p>\n\n<p>\nr = 32\n<\/p>\n\n<h3>Krok 4: Obliczenie, o ile wi\u0119ksza musi by\u0107 miesi\u0119czna wp\u0142ata<\/h3>\n\n<p>Dotychczasowa r\u00f3\u017cnica wynosi\u0142a 25 z\u0142.<\/p>\n\n<p>\nNowa r\u00f3\u017cnica \u2013 stara r\u00f3\u017cnica = 32 \u2212 25 = <strong>7 z\u0142<\/strong>\n<\/p>\n\n<h3>Wniosek<\/h3>\n\n<p>Pani Joanna powinna zwi\u0119kszy\u0107 miesi\u0119czny przyrost wp\u0142at o <strong>7 z\u0142<\/strong>.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 35. zbi\u00f3r zada\u0144 CKE (zadanie otwarte) Pani Joanna postanowi\u0142a systematycznie oszcz\u0119dza\u0107 i co miesi\u0105c na swoje subkonto odk\u0142ada\u0107 pewn\u0105 sum\u0119 pieni\u0119dzy. Pierwszego czerwca 2020 roku wp\u0142aci\u0142a 300 z\u0142otych. Pierwszego dnia ka\u017cdego miesi\u0105ca wp\u0142aca o 25 z\u0142 wi\u0119cej ni\u017c w miesi\u0105cu poprzednim. zadanie 35.1. (1pkt) Oblicz kwot\u0119, jak\u0105 pani Joanna wp\u0142aci\u0142a na subkonto pierwszego czerwca [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"saved_in_kubio":false,"_uag_custom_page_level_css":"","_themeisle_gutenberg_block_has_review":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[25,204,81,83,146],"tags":[23,205,145],"class_list":["post-1478","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-rozne","category-zadania-maturalne","category-zadania-tematami","category-zbior-zadan-cke","tag-ciag-arytmetyczny","tag-rozne","tag-zbior-zadan-cke"],"jetpack_featured_media_url":"","uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"kubio-fullhd":false,"woocommerce_thumbnail":false,"woocommerce_single":false,"woocommerce_gallery_thumbnail":false},"uagb_author_info":{"display_name":"adminmymatma","author_link":"https:\/\/mymatma.pl\/?author=1"},"uagb_comment_info":0,"uagb_excerpt":"zadanie 35. zbi\u00f3r zada\u0144 CKE (zadanie otwarte) Pani Joanna postanowi\u0142a systematycznie oszcz\u0119dza\u0107 i co miesi\u0105c na swoje subkonto odk\u0142ada\u0107 pewn\u0105 sum\u0119 pieni\u0119dzy. Pierwszego czerwca 2020 roku wp\u0142aci\u0142a 300 z\u0142otych. Pierwszego dnia ka\u017cdego miesi\u0105ca wp\u0142aca o 25 z\u0142 wi\u0119cej ni\u017c w miesi\u0105cu poprzednim. zadanie 35.1. (1pkt) Oblicz kwot\u0119, jak\u0105 pani Joanna wp\u0142aci\u0142a na subkonto pierwszego czerwca&hellip;","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1478","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1478"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1478\/revisions"}],"predecessor-version":[{"id":1483,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1478\/revisions\/1483"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1478"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1478"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1478"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}