AMC10 2019 B

AMC10 2019 B · Q11

AMC10 2019 B · Q11. It mainly tests Linear equations, Ratios & proportions.

Two jars each contain the same number of marbles, and every marble is either blue or green. In Jar 1 the ratio of blue to green marbles is 9:1, and the ratio of blue to green marbles in Jar 2 is 8:1. There are 95 green marbles in all. How many more blue marbles are in Jar 1 than in Jar 2?

有两个罐子，每个罐子里有相同数量的弹珠，每颗弹珠要么是蓝色的，要么是绿色的。罐子1中蓝色的弹珠与绿色的弹珠之比是9:1，罐子2中蓝色的弹珠与绿色的弹珠之比是8:1。总共有95颗绿色的弹珠。罐子1中蓝色的弹珠比罐子2中多多少？

(A) 5 5

(B) 10 10

(D) 45 45

(E) 50 50

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): Let $x$ be the number of green marbles in Jar 1. Then there are $95-x$ green marbles in Jar 2. Jar 1 contains $9x$ blue marbles and $10x$ marbles in all, and Jar 2 contains $8(95-x)$ blue marbles and $9(95-x)$ marbles in all. Because the jars contain the same number of marbles, $10x = 9(95-x)$, and this equation has the solution $x = 45$. Therefore Jar 1 contains $9\cdot 45 = 405$ blue marbles, and Jar 2 contains $8(95-45) = 400$ blue marbles. Jar 1 contains $405-400 = 5$ more blue marbles than does Jar 2.

答案（A）：设$x$为罐1中绿色弹珠的数量，则罐2中绿色弹珠为$95-x$。罐1中有$9x$个蓝色弹珠，总共有$10x$个弹珠；罐2中有$8(95-x)$个蓝色弹珠，总共有$9(95-x)$个弹珠。由于两只罐中的弹珠总数相同，有$10x = 9(95-x)$，解得$x = 45$。因此罐1中蓝色弹珠为$9\cdot 45 = 405$个，罐2中蓝色弹珠为$8(95-45) = 400$个。罐1比罐2多$405-400 = 5$个蓝色弹珠。

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