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.
选项
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\(B\)。