某服装店有甲、乙、丙、丁四个缝制小组。甲组每天能缝制5件上衣或6条裤子：乙组每天能缝制6件上衣或7条裤子：丙组每天能缝制7件上衣或8条裤子；丁组每天能缝制8件上衣或9条裤子。每组每天要么缝制上衣，要么缝制裤子，不能弄混。订单要求上衣和裤子必须配套（每套衣服包括一件上衣和一条裤子）。做好合理安排，该服装店15天最多能缝制（ ）套衣服。
- A.208
- B.209
- C.210
- D.211
正确答案及解析
正确答案
解析
本题考查数学应用能力
根据题意，甲、乙、丙、丁四组做上衣和裤子的效率之比分别为5/6、6/7、7/8、8/9，并且依次增加。因此，丁组做上衣效率更高，甲组做裤子效率更高。为此，安排甲组15天全做裤子，丁组15天全做上衣。
设乙组用x天做上衣，15-x天做裤子；丙组用y天做上衣，15-y天做裤子，为使上衣和裤子配套，则有
0+6x+7y+8×15=6×15+7(15-x)+8(15-y)+0
所以，13x+15y=13×15，y=13-13x/15
15天共做套数6x+7y+8×15=6x+7(13-13x/15)+120=211-x/15
只有在x=0时，最多可做211套。
此时，y=13，即甲乙丙丁四组分别用0、0、13、15天做上衣，用15、15、2、0天做裤子。
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