AMC12 2014 B

AMC12 2014 B · Q6

AMC12 2014 B · Q6. It mainly tests Linear equations, Fractions.

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 $\frac{3}{4}$ 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?

Ed 和 Ann 午餐时都点了柠檬水。Ed 点了常规尺寸。Ann 点了大杯柠檬水，比常规尺寸多 $50\%$。两人各自喝掉 $\frac{3}{4}$ 的饮料后，Ann 给了 Ed 她剩下柠檬水的三分之一，外加 2 盎司。当他们喝完柠檬水时，发现两人喝的量相同。他们总共喝了多少盎司的柠檬水？

(A) 30 30

(B) 32 32

(D) 40 40

(E) 50 50

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Let $a$ be the amount in a regular lemonade. Then a large lemonade holds $\frac{3}{2}a$, and Ann had $\frac{1}{4}\cdot\frac{3}{2}a-\frac{3}{8}a$ lemonade left right before she gave Ed part of her drink. She gave him $\frac{1}{3}\cdot\frac{3}{8}a+2=\frac{1}{8}a+2$ ounces. Because Ann and Ed drank the same amount of lemonade, it follows that $a+\left(\frac{1}{8}a+2\right)=\frac{3}{2}a-\left(\frac{1}{8}a+2\right)$, and $4=\frac{1}{4}a$. Thus $a=16$ ounces, $\frac{3}{2}a=24$ ounces, and together they drank $16+24=40$ ounces.

答案（D）：设 $a$ 为一杯普通柠檬水的容量，则一杯大杯柠檬水的容量为 $\frac{3}{2}a$。在安把饮料分给埃德之前，她还剩下 $\frac{1}{4}\cdot\frac{3}{2}a-\frac{3}{8}a$ 的柠檬水。她给了他 $\frac{1}{3}\cdot\frac{3}{8}a+2=\frac{1}{8}a+2$ 盎司。因为安和埃德喝的柠檬水量相同，所以有 $a+\left(\frac{1}{8}a+2\right)=\frac{3}{2}a-\left(\frac{1}{8}a+2\right)$，从而得到 $4=\frac{1}{4}a$。因此 $a=16$ 盎司，$\frac{3}{2}a=24$ 盎司，他们一共喝了 $16+24=40$ 盎司。

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