题目

Marcy bought one pair of jeans at 70% off and one blouse at 40% off. If she paid $12 more for the blouse than for the jeans, and she spent a total of $84, what was the original price of the jeans?


选项

A.

76

B.

96

C.

100

D.

120

E.

124

解析

要解决这个问题,先设定以下变量: J = 牛仔裤原价 B = 衬衫原价 接下来建立方程组,注意“七折优惠”等价于原价的 100%−70%=30%,即 0.3 倍原价: 0.3J+12=0.6B 0.3J+0.6B=84 现在用你最熟悉的方法解方程组——比如将方程变形后相减: 0.3J + 12 = 0.6B 0.3J - 84 = -0.6B 0 + 96 = 1.2B B = 80 将衬衫价格代回原方程,即可求出牛仔裤价格: 0.3J + 12 = 0.6B 0.3J + 12 = 48 0.3J = 36 J = 120 --- 另一种方法:先设打折后牛仔裤的价格为 $x$,可列出方程: x + (x + 12) = 84 2x + 12 = 84 2x = 72 x = 36 再将打折后价格代入“打折后价格 = 原价 × (100% - 折扣百分比)”: 36 = 0.3P 360 = 3P 120 = P 因此,选项 D 正确!
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