1983 AMC 12 第 7 题

Question

爱丽丝以比标价低

\$10

的价格卖出一件商品，并得到售价的

10\%

作为佣金。鲍勃以比标价低

\$20

的价格卖出同一件商品，并得到售价的

20\%

作为佣金。若两人的佣金相同，则标价为

Alice sells an item at

\$10

less than the list price and receives

10\%

of her selling price as her commission. Bob sells the same item at

\$20

less than the list price and receives

20\%

of his selling price as his commission. If they both get the same commission, then the list price is

\$20

\$30

\$50

\$70

\$100

设标价为

L

，用

L

分别表示两人的佣金

Let

L

be the list price and write each commission in terms of

L

令

0.1(L-10)

等于

0.2(L-20)

Set

0.1(L-10)

equal to

0.2(L-20)

若标价为

L

，由佣金相等可得

0.1(L-10)=0.2(L-20)

。两边乘以

10

并求解，得到

L-10=2L-40

，所以

L=30

。

所以正确答案是 B。

If the list price is

L,

equality of commissions gives

0.1(L-10)=0.2(L-20).

Multiplying by

10

and solving gives

L-10=2L-40,

so

L=30.

Therefore, the correct answer is B.

其他年份的第 7 题