题目

The total cost of 3 bananas, 2 apples, and 1 mango is $3.50. The total cost of 3 bananas, 2 apples, and 1 papaya is $4.20. The ratio of the cost of a mango to the cost of a papaya is 3 : 5.


Quantity A

The cost of a papaya


Quantity B

$2.00

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

3根香蕉、2个苹果和1个芒果的总费用是3.50美元。3根香蕉、2个苹果和1个木瓜的总费用是4.20美元。芒果与木瓜的价格比是3:5。设芒果的价格为\(3x\)美元,因为芒果与木瓜的价格比是\(3:5\),所以木瓜的价格为\(5x\)美元。 根据已知条件可得: \((3\)根香蕉\( + 2\)个苹果\(+ 1\)个芒果\()=3.50\) ,即 \(3\)根香蕉\( + 2\)个苹果\(+3x=3.50\) \((3\)根香蕉\( + 2\)个苹果\(+ 1\)个木瓜\() = 4.20\),即\(3\)根香蕉\( + 2\)个苹果\(+5x=4.20\) 用第二个式子减去第一个式子可得: \[ \begin{align*} (3\)根香蕉\( + 2\)个苹果\(+5x)-(3\)根香蕉\( + 2\)个苹果\(+3x)&=4.20 - 3.50\\ 2x&=0.7\\ x& = 0.35 \end{align*} \] 所以木瓜的价格\(5x=5\times0.35 = 1.75\)美元 因为\(1.75<2.00\),所以数量\(B\)更大,答案是\(B\)。
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