Question

Ed 和 Ann 午餐时都喝柠檬水。Ed 点了普通杯。Ann 点了大杯，比普通杯多 $50\%$ 。两人都喝掉各自饮料的 $\tfrac34$ 后，Ann 把自己剩下饮料的三分之一再加 $2$ 盎司给了 Ed。当他们喝完柠檬水时，发现两人喝掉的量相同。他们一共喝了多少盎司柠檬水？

Ed and Ann both have lemonade with their lunch. Ed orders the regular size. Ann gets the large lemonade, which is $50\%$ more than the regular. After both consume $\tfrac34$ of their drinks, Ann gives Ed a third of what she has left, and $2$ additional ounces. When they finish their lemonades they realize that they both drank the same amount. How many ounces of lemonade did they drink together?

$30$

$32$

$36$

$40$

$50$

答案：D

知识点：分数一次方程

难度评级：1460

解答：

设普通杯柠檬水为 $a$ 盎司，则 Ann 的大杯为 $\tfrac32 a$ 。每人喝掉 $\tfrac34$ 后，Ann 剩下 $\tfrac14\cdot\tfrac32 a = \tfrac38 a$ ，她给 Ed $\tfrac13\cdot\tfrac38 a + 2 = \tfrac18 a + 2$ 盎司。

Ed 喝了自己的全部 $a$ 盎司再加上这份转给他的饮料，Ann 喝了 $\tfrac32 a$ 减去这份饮料。令二者相等：得 $4 = \tfrac14 a$ ，所以 $a = 16$ 。 $a + \left(\tfrac18 a + 2\right) = \tfrac32 a - \left(\tfrac18 a + 2\right),$

于是 Ed 喝了 $16$ 盎司，Ann 喝了 $24$ 盎司，总共 $40$ 盎司。

所以正确答案是 D。

Let a regular lemonade hold $a$ ounces, so Ann's large holds $\tfrac32 a.$ After each drinks $\tfrac34,$ Ann has $\tfrac14\cdot\tfrac32 a = \tfrac38 a$ left, and she gives Ed $\tfrac13\cdot\tfrac38 a + 2 = \tfrac18 a + 2$ ounces.

Ed drinks his full $a$ ounces plus that gift, and Ann drinks her $\tfrac32 a$ minus the gift. Setting these equal, $a + \left(\tfrac18 a + 2\right) = \tfrac32 a - \left(\tfrac18 a + 2\right),$ which gives $4 = \tfrac14 a,$ so $a = 16.$

Then Ed drank $16$ ounces and Ann drank $24$ ounces, for a total of $40$ ounces.

Thus, the correct answer is D.

2014 AMC 12B 第 6 题

答案：D

难度评级：1460

解答：

其他年份的第 6 题