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?
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
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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!