Đại lượng tỉ lệ nghịch - Bài tập nâng cao

Home Lớp 7 Toán lớp 7 - Sách kết nối tri thức Bài 23: Đại lượng tỉ lệ nghịchBài tập nâng cao

{"common":{"save":0,"post_id":"5799","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8303","post_id":"5799","mon_id":"1158532","chapter_id":"1158659","question":"Bi\u1ebft x t\u1ec9 l\u1ec7 thu\u1eadn v\u1edbi y theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 là 3, y t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi z theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 là 4. H\u1ecfi x t\u1ec9 l\u1ec7 thu\u1eadn hay t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi z và h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 là bao nhiêu?<\/p>","options":["A. <\/strong>x t\u1ec9 l\u1ec7 thu\u1eadn v\u1edbi z theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 12","B. <\/strong>x t\u1ec9 l\u1ec7 thu\u1eadn v\u1edbi z theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 $\\dfrac{3}{4}$<\/span>","C. <\/strong>x t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi z theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 12","D. <\/strong>x t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi z theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 $\\dfrac{1}{12}$<\/span>"],"correct":"3","level":"3","hint":"","answer":"Vì x t\u1ec9 l\u1ec7 thu\u1eadn v\u1edbi y theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 là 3 nên x = 3y<\/p>Vì y t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi z theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 là 4 nên y = $\\dfrac{4}{z}$<\/span><\/p>Suy ra x = 3y = 3 . $\\dfrac{4}{z}$<\/span> = $\\dfrac{12}{z}$<\/span> hay x = $\\dfrac{12}{z}$<\/span><\/p>V\u1eady x t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi z theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 12<\/p>\u0110áp án \u0111úng là C. <\/strong>x t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi z theo h\u1ec7 s\u1ed1 t\u1ec9 l\u1ec7 12<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-05-28 10:29:28","option_type":"math","len":0},{"id":"8365","post_id":"5799","mon_id":"1158532","chapter_id":"1158659","question":"M\u1ed9t ng\u01b0\u1eddi mua 65 qu\u1ea3 tr\u1ee9ng gà g\u1ed3m ba lo\u1ea1i: lo\u1ea1i m\u1ed9t giá 4 nghìn \u0111\u1ed3ng m\u1ed9t qu\u1ea3, lo\u1ea1i hai giá 3 nghìn \u0111\u1ed3ng m\u1ed9t qu\u1ea3, lo\u1ea1i ba giá 2 nghìn \u0111\u1ed3ng m\u1ed9t qu\u1ea3. H\u1ecfi ng\u01b0\u1eddi \u0111ó mua bao nhiêu qu\u1ea3 tr\u1ee9ng m\u1ed7i lo\u1ea1i, bi\u1ebft s\u1ed1 ti\u1ec1n mà ng\u01b0\u1eddi \u0111ó ph\u1ea3i tr\u1ea3 cho m\u1ed7i lo\u1ea1i tr\u1ee9ng là nh\u01b0 nhau?<\/p>","options":["A. <\/strong>Lo\u1ea1i m\u1ed9t 15 qu\u1ea3, lo\u1ea1i hai 20 qu\u1ea3, lo\u1ea1i ba 30 qu\u1ea3","B. <\/strong>Lo\u1ea1i m\u1ed9t 20 qu\u1ea3, lo\u1ea1i hai 15 qu\u1ea3, lo\u1ea1i ba 30 qu\u1ea3","C. <\/strong>Lo\u1ea1i m\u1ed9t 12 qu\u1ea3, lo\u1ea1i hai 18 qu\u1ea3, lo\u1ea1i ba 35 qu\u1ea3","D. <\/strong>Lo\u1ea1i m\u1ed9t 30 qu\u1ea3, lo\u1ea1i hai 20 qu\u1ea3, lo\u1ea1i ba 15 qu\u1ea3"],"correct":"1","level":"3","hint":"","answer":"G\u1ecdi x, y, z l\u1ea7n l\u01b0\u1ee3t là s\u1ed1 qu\u1ea3 tr\u1ee9ng lo\u1ea1i m\u1ed9t, lo\u1ea1i hai, lo\u1ea1i ba mà ng\u01b0\u1eddi \u0111ó mua (x, y, z ∈ N*)<\/p>S\u1ed1 ti\u1ec1n mua tr\u1ee9ng lo\u1ea1i m\u1ed9t, lo\u1ea1i hai, lo\u1ea1i ba l\u1ea7n l\u01b0\u1ee3t là 4 . x ; 3 . y ;  2 . z (nghìn \u0111\u1ed3ng)<\/p>Vì ng\u01b0\u1eddi \u0111ó mua 65 qu\u1ea3 tr\u1ee9ng nên x + y + z  = 65<\/span> (qu\u1ea3)<\/p>Vì s\u1ed1 ti\u1ec1n mà ng\u01b0\u1eddi \u0111ó ph\u1ea3i tr\u1ea3 cho m\u1ed7i lo\u1ea1i tr\u1ee9ng là nh\u01b0 nhau nên<\/p>4 . x = 3 . y = 2 . z hay $\\dfrac{x}{\\dfrac{1}{4}}=\\dfrac{y}{\\dfrac{1}{3}}=\\dfrac{z}{\\dfrac{1}{2}}$<\/span><\/span><\/p>Áp d\u1ee5ng tính ch\u1ea5t c\u1ee7a dãy t\u1ec9 s\u1ed1 b\u1ea3ng nhau ta có:<\/p>$\\dfrac{x}{\\dfrac{1}{4}}=\\dfrac{y}{\\dfrac{1}{3}}=\\dfrac{z}{\\dfrac{1}{2}}=\\dfrac{x+y+z}{\\dfrac{1}{4}+\\dfrac{1}{3}+\\dfrac{1}{2}}=\\dfrac{65}{\\dfrac{13}{12}}=60$<\/span><\/p>Suy ra x = 60 . $\\dfrac{1}{4}$<\/span> = 15 (qu\u1ea3) ;  y = 60 . $\\dfrac{1}{3}$<\/span> = 20 (qu\u1ea3) ; z = 60 . $\\dfrac{1}{2}$<\/span> = 30 (qu\u1ea3)<\/p>V\u1eady \u0111áp án \u0111úng là A. <\/strong>Lo\u1ea1i m\u1ed9t 15 qu\u1ea3, lo\u1ea1i hai 20 qu\u1ea3, lo\u1ea1i ba 30 qu\u1ea3<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-05-29 04:03:18","option_type":"txt","len":3},{"id":"8367","post_id":"5799","mon_id":"1158532","chapter_id":"1158659","question":"B\u1ed1n ng\u01b0\u1eddi th\u1ee3 cùng làm s\u1ebd xây xong m\u1ed9t b\u1ee9c t\u01b0\u1eddng trong 10 ngày. H\u1ecfi n\u0103m ng\u01b0\u1eddi th\u1ee3 cùng làm s\u1ebd xây xong b\u1ee9c t\u01b0\u1eddng trong bao nhiêu ngày? (bi\u1ebft n\u0103ng su\u1ea5t c\u1ee7a m\u1ed7i ng\u01b0\u1eddi th\u1ee3 là nh\u01b0 nhau)<\/p>","options":["9 ngày","8 ngày","7 ngày","10 ngày"],"correct":"2","level":"3","hint":"","answer":"G\u1ecdi x (ngày) là th\u1eddi gian \u0111\u1ec3 5 ng\u01b0\u1eddi th\u1ee3 cùng xây xong m\u1ed9t b\u1ee9c t\u01b0\u1eddng (x > 0).<\/p>Vì n\u0103ng su\u1ea5t c\u1ee7a m\u1ed7i ng\u01b0\u1eddi là nh\u01b0 nhau nên s\u1ed1 ng\u01b0\u1eddi th\u1ee3 và th\u1eddi gian \u0111\u1ec3 h\u1ecd xây xong m\u1ed9t b\u1ee9c t\u01b0\u1eddng là hai \u0111\u1ea1i l\u01b0\u1ee3ng t\u1ec9 l\u1ec7 ngh\u1ecbch.<\/p>Do \u0111ó ta có: 4 . 10 = 5 . x<\/span><\/p>Suy ra x = $\\dfrac{4.10}{5}=8$<\/span> (ngày)<\/p>V\u1eady th\u1eddi gian \u0111\u1ec3 5 ng\u01b0\u1eddi th\u1ee3 cùng xây xong m\u1ed9t b\u1ee9c t\u01b0\u1eddng là 8 ngày<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-05-29 04:10:30","option_type":"txt","len":1}]}