题目内容
某粮油超市平时每天都将一定数量的某些品种的粮食进行包装以便出售，已知每天包装大黄米的质量是包装江米质量的
倍，且每天包装大黄米和江米的质量之和为45千克．
(1)求平均每天包装大黄米和江米的质量各是多
少千克?
(2)为迎接今年6月20日的“端午节”，该超市决定在节日前20天增加每天包装大黄米和江米的质量，二者的包装质量与天数的变化情况如图所示，节日后又恢复到原来每天的包装
质量．分别求出在这20天内每天包装大黄米和江米的质量随天数变化的函数关系式，并写出自变量的取值范围．
(3)假设该超市每天都会将当天包装后的大黄米和江米全部出售，已知大黄米成本价为每千克7.9元，江米成本价为每千克9.5元，二者包装费用平均每千克均为0.5元，大黄米售价为每千克10元，江米售价为每千克12元，那么在这20天中有哪几天销售大黄米和江米的利润之和大于120元? [总利润=售价额－成本－包装费用]
 |
解：(1)解法一：
设平均每天包装大黄米和江米的质量分别为a千克和b千克， ··············································· 1分
则 
，解得
．····························································································· 3分
答：平均每天包装大黄米和江米的质量分别为25千克和20千克． ········································ 4分
解法二：
设平均每天包装大黄米的质量为a千克，那么包装江米的质量（45
a）千克， ····················· 1分
则 
， 解得 a=25，所以4525=20． ····························································· 3分
答：平均每天包装大黄米和江米的质量分别为25千克和20千克． ········································ 4分
（2）观察图象，可设平均每天包装大黄米的质量与天数的关系式为
，平均每天包装江米的质量与天数的关系式为
．
①当
时，
由题意的图象过点
，
．
则可列方程组为
，解得
，
∴
．······················································································································· 5分
由题意的图象过点
，
．
则可列方程组为
，解得
,
∴
．···················································································································· 6分
②当
时，
由题意的图象过点，
．
则可列方程组为
，解得
，
∴
．··················································································································· 7分
由题意的图象过点，
．
则可列方程组为
，解得
，
∴
．················································································································ 8分
∴
， 
． ···························· 9分 (3)设第
天销售的总利润为
元，
①当时，
．
由题意
，∴
，
∴x的取值范围为
，
由题意知
．································································································ 10分
②当时，
．
由题意
，∴
，
∴x的取值范围为
．
由题意知
．················································································································· 11分
答：由①、②可知在第11，12，13，14，15，16天中销售大黄米和江米的总利润大于120元． 12分
状元坊全程突破导练测系列答案
直通贵州名校周测月考直通名校系列答案
．
．其中
满足一元二次方程
．一个几何体的三视图如图所示，则这个几何体是（ ）
|
| A． | 圆柱 | B． | 圆锥 | C． | 长方体 | D． | 正方体 |
如图，AB∥CD，∠A=50°，则∠1的大小是（ ）
|
| A． | 50° | B． | 120° | C． | 130° | D． | 150° |
÷（
﹣1），其中x=2﹣
．