數學題:小奧計劃到外地旅行數天,他在計算每天可使用的旅費,如果每天用六百元,欠四百元;用五百元,餘下五百元.即多少天?

問題: 小奧計劃到外地旅行數天,他在計算每天可使用的旅費,如果每天用六百元,欠四百元;
用五百元,餘下五百元.即多少天?

回答:
設小奧到外地旅行 n 天;每天需用 z 元,
zn - 600n = -400
zn - 600n + 400 = 0 --------(1)

zn - 500n = 500
zn - 500n - 500 = 0 ---------(2)

(1) = (2)
zn - 600n + 400 = zn - 500n - 500
400 + 500 = 600n - 500n
900 = 100n
900 / 100 = n
9 = n
n = 9
∴他共到外地旅行 9 天。

设:即X天
600X-400=500X+500
100X=900
X=9

Let the money he used per day is x, the total money he has is y
y-600x=-400 ---------(1)
500X+500=y -------- (2)
With these two equations, we can know that:
500X+500-600X=-400
-100X=-900
x=9

Therefore, the trip is lasted for 9 days

500x+500=600x-400
900=100x
x=9