AMC10 2007 A

AMC10 2007 A · Q5

AMC10 2007 A · Q5. It mainly tests Systems of equations.

A school store sells $7$ pencils and $8$ notebooks for $\$4.15$. It also sells $5$ pencils and $3$ notebooks for $\$1.77$. How much do $16$ pencils and $10$ notebooks cost?

$7$支铅笔和 $8$本笔记本售价 $\$4.15$。$5$支铅笔和 $3$本笔记本售价 $\$1.77$。$16$支铅笔和 $10$本笔记本售价多少？

(A) $\$$4.76 $\$$4.76

(B) $\$$5.84 $\$$5.84

(D) $\$$6.16 $\$$6.16

(E) $\$$6.32 $\$$6.32

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Let $p$ be the cost in cents of a pencil and $n$ be the cost in cents of a notebook. Then $7p + 8n = 415$ and $5p + 3n = 177$. The solution of this pair of equations is $p = 9$ and $n = 44$. So the cost of 16 pencils and 10 notebooks is $16(9) + 10(44) = 584$ cents, or \$5.84.

答案（B）：设$p$为一支铅笔的价格（单位：美分），$n$为一本笔记本的价格（单位：美分）。则 $7p + 8n = 415$，且$5p + 3n = 177$。该方程组的解为$p = 9$、$n = 44$。因此，16支铅笔和10本笔记本的总价为$16(9) + 10(44) = 584$美分，即 \$5.84。

Topics

AL.002 Systems of equations