12. 解:(1)設(shè)總廠原來每周制作帳篷千頂,分廠原來每周制作帳篷千頂.
由題意,得······················································································· 3分
解得所以(千頂),(千頂).
答:在趕制帳篷的一周內(nèi),總廠、分廠各生產(chǎn)帳篷8千頂、6千頂.····························· 6分
(2)設(shè)從(甲市)總廠調(diào)配千頂帳篷到災(zāi)區(qū)的地,則總廠調(diào)配到災(zāi)區(qū)地的帳篷為千頂,(乙市)分廠調(diào)配到災(zāi)區(qū)兩地的帳篷分別為千頂.
甲、乙兩市所需運(yùn)送帳篷的車輛總數(shù)為輛.······························································· 8分
由題意,得.
即.······················································································ 10分
因?yàn)?sub>,所以隨的增大而減小.
所以,當(dāng)時(shí),有最小值60.
答:從總廠運(yùn)送到災(zāi)區(qū)地帳篷8千頂,從分廠運(yùn)送到災(zāi)區(qū)兩地帳篷分別為1千頂、5千頂時(shí)所用車輛最少,最少的車輛為60輛. 12分
11. 解:設(shè)生產(chǎn)奧運(yùn)會標(biāo)志x套,生產(chǎn)奧運(yùn)會吉祥物y套.根據(jù)題意,得
…………………………………………2分
①×2-②得:5x=10000.
∴ x=2000. ………………………………………………………………6分
把x=2000代入①得:5y=12000.
∴ y=2400.
答:該廠能生產(chǎn)奧運(yùn)會標(biāo)志2000套,生產(chǎn)奧運(yùn)會吉祥物2400套.……8分
10. (1)甲隊(duì)行進(jìn)了2小時(shí),乙隊(duì)行進(jìn)了2.5小時(shí).
設(shè)乙隊(duì)的速度為x,則甲隊(duì)為1.5x + 5.
由題意得方程 2.5x +(1.5x + 5)×2 + 1 = 176.
整理得 5.5x = 165, 解得 x = 30.
∴ 1.5x + 5 = 1.5×30 + 5 = 50.
即甲隊(duì)趕路的速度為50 km∕h,乙隊(duì)趕路的速度為30 km∕h.
(2)設(shè)若由乙隊(duì)單獨(dú)施工,需x小時(shí)才能完成.
則由題意有 6×()+ 5.5×= 1.
解得 x = 11.
即乙隊(duì)單獨(dú)做,需要11小時(shí)才能完成任務(wù).
9. 解:(1)設(shè)小明他們一共了個(gè)成人,個(gè)學(xué)生,
································································································· 4分
····················································································································· 6分
答:小明他們一共去了7個(gè)成人,4個(gè)學(xué)生.································································ 7分
(2)若按14人購買團(tuán)體票,則共需(元)
(元).
購買團(tuán)體票可省24元.····························································································· 3分
8. 解 ∵
由②得,③ ······························································································· 2分
將③代入①,得.解得.代入③,得.
∴原方程組的解為 6分
7. 解:設(shè)生產(chǎn)奧運(yùn)會標(biāo)志x套,生產(chǎn)奧運(yùn)會吉祥物y套,得
解得,答略.
6. .解:設(shè)原計(jì)劃每天挖土石方x萬立方米,增調(diào)人員和設(shè)備后每天挖y萬立方米················ 1分
可列出方程組:···································································· 5分
解之得:
答:原計(jì)劃每天挖土石方1.3萬立方米,增調(diào)人員和設(shè)備后每天挖3.6萬立方米······ 8分
5.
解:設(shè)A種帳篷x頂,B種帳篷y頂,根據(jù)題意,列方程組
……………………………………………4分
解,得 ………………………………………………6分
∴ A種帳篷400頂,B種帳篷200頂. ………………………………………7分
4.
3. 解:(1)a=2,b=0.125
(2)圖略
(3)設(shè)一等獎(jiǎng)x人,二等獎(jiǎng)y人,依題意得
解得所以他們共獲獎(jiǎng)金=50×9+30×20=1050元
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