题目

Yesterday, a certain school had an equal number of boys and girls. Today, 18 boys left the school, and the ratio of the number of boys to girls is now 3 to 4.


Quantity A

Number of boys in the school now


Quantity B

72

选项

A.

Quantity A is greater.

B.

Quantity B is greater.

C.

The two quantities are equal.

D.

The relationship cannot be determined from the information given.

解析

昨天,某所学校的男生和女生数量相等。今天,有18名男生离开了学校,现在男生与女生的人数比是3:4。 设昨天学校里男生和女生的数量都为\(x\)名。今天男生离开了\(18\)人后,男生的数量为\((x - 18)\)名,此时男、女生人数比为\(3:4\),即\(\frac{x-18}{x}=\frac{3}{4}\)。 根据上述等式交叉相乘可得: \(4(x - 18)=3x\) 展开括号:\(4x-72 = 3x\) 移项可得:\(4x-3x=72\) 解得:\(x = 72\) 那么现在男生的数量为\(x-18=72 - 18=54\)(名) 因为\(54<72\),所以数量\(B\)更大,答案是\(B\)。
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