题目

Roy sells homegrown cucumbers and peppers at the local farmer's market. He charges one price for each cucumber and another price for each pepper. If Roy charges $6.00 for 3 cucumbers and 8 peppers and $3.20 for 2 cucumbers and 4 peppers, how much does he charge for 3 cucumbers and 5 peppers?


选项

A.

$3.80

B.

$4.20

C.

$4.60

D.

$5.10

E.

$5.20

解析

设黄瓜的单价为\( c \)美元,甜椒的单价为\( p \)美元,已知\( c \neq p \)。 ### 已知条件: 1. 3根黄瓜和8个甜椒售价6.00美元: \[3c + 8p = 6 \quad ---(1)\] 2. 2根黄瓜和4个甜椒售价3.20美元: \[2c + 4p = 3.2\] 将此式两边乘以2,得: \[4c + 8p = 6.4 \quad ---(2)\] ### 求解单价: 用式(2)减去式(1): \[ \begin{align*} (4c + 8p) - (3c + 8p) &= 6.4 - 6 \\ c &= 0.4 \end{align*} \] 将\( c = 0.4 \)代入\( 2c + 4p = 3.2 \),得: \[2×0.4 + 4p = 3.2 \implies 4p = 2.4 \implies p = 0.6\] ### 计算3根黄瓜和5个甜椒的价格: \[3c + 5p = 3×0.4 + 5×0.6 = 1.2 + 3.0 = 4.20\] 答案:B
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