Combined price of large and small shirts

Let price of a large shirt be $p$, small shirt be $p - 50$. Number of large shirts = $\frac{5000}{p}$, small shirts = $\frac{1800}{p - 50}$.

Total shirts = 64: $\frac{5000}{p} + \frac{1800}{p - 50} = 64$

Divide by 8: $\frac{625}{p - 50} + \frac{625 - 625}{p} \dots$ $\frac{625(p-50) + 225p}{p(p-50)} = 8$ $850p - 31250 = 8p^2 - 400p$ $8p^2 - 1250p + 31250 = 0 \implies 4p^2 - 625p + 15625 = 0$ $(p - 125)(4p - 125) = 0$

If $p = 125$, price of small shirt = $75$. Price of large and small shirt together = $125 + 75 = 200$.