Câu hỏi của Trần Đức Mạnh

Question

A book costs £3.40 and a magazine costs £1.60. If Clara spends exactly £23 on books and magazines, how many of each does she buy?

Akai Haruma · Accepted Answer

Lời giải:

Gọi số sách mà Clara đã mua là $a$ và số tạp chí đã mua là $b$ ($a,b\in\mathbb{N}^*$ )

Theo bài ra ta có: $3,4a+1,6b=23$

$\Rightarrow 3,4a=23-1,6b\leq 23-1,6.1$ do $b\geq 1$

hay $3,4a\leq 21,4\Rightarrow a\leq \frac{21,4}{3,4}\Rightarrow a\leq 6$

Vì $a\in\mathbb{N}^*\Rightarrow a\in\left\{1;2;3;4;5;6\right\}$

Nếu $a=1\Rightarrow b=\frac{23-3,4}{1,6}=\frac{49}{4}\not\in\mathbb{N}^*$ (loại)

Nếu $a=2\Rightarrow b=\frac{23-3,4.2}{1,6}=\frac{81}{8}\not\in\mathbb{N}^*$ (loại)

Nếu $a=3\Rightarrow b=\frac{23-3,4.3}{1,6}=8$ (thỏa mãn)

Nếu $a=4\Rightarrow b=\frac{23-3,4.4}{1,6}=\frac{47}{8}\not\in\mathbb{N}$ (loại)

Nếu $a=5\Rightarrow b=\frac{23-3,4.5}{1,6}=\frac{15}{4}\not\in\mathbb{N}^*$ (loại)

Nếu $a=6\Rightarrow b=\frac{23-3,4.6}{1,6}=\frac{13}{8}\not\in\mathbb{N}^*$ (loại )

Vậy Clara mua $3$ quyển sách và $8$ quyển tạp chí.

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