問功課系列 (9) 數學題：請用一般四則運算方法計算x和y的數值

Solve (x + 23)/(y + 23) – x/y = 4%.

Let y = t , for all t inＣ\{0 , – 23}
Then (x + 23)/(t + 23) – x/t = 4%
((x + 23)t – x(t + 23))/(t(t + 23)) = 0.04
(tx + 23t – tx – 23x)/(t² + 23t) = 1/25
575t – 575x = t² + 23t
575x = 552t – t²
x = (552t – t²)575

Therefore, there are infinitely many solutions of x and y.
Taking t = 1 as a case, we have
　╭
　│x = 551/575
─┤
　│y = 1
　╰
In fact the general expression is
　╭
　│x = (552t – t²)575
─┤　　　　　　　　, for all t inＣ\{0 , – 23}
　│y = t
　╰

　╭
　│x = (552t – t²)575
─┤　　　　　　　　, for all t in C\{0 , – 23}
　│y = t
　╰