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?
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