Question

A restaurant charged one customer $28.20 for 3 small dishes and 5 large dishes and charged another customer $23.30 for 4 small dishes and 3 small dishes. What will 2 small and 4 large dishes cost?

Answer 1

Let s and l be the price of small and large dishes. The first equation is

$3s+5l = 28.20$

While the second equation is

$4s+3l=23.30$

(I assume that you meant "4 small dishes and 3 large dishes")

If we multiply the first equation by 4 and the second by 3 we have

$\begin{cases}12s+20l=112.8\\12s+9l=69.9\end{cases}$

Subtract the two equation and you have

$11l = 42.9 \iff l = 3.9$

Substitute this value in one of the equation to derive

$3s+5\cdot 3.9 = 28.20 \iff s=2.9$

So, one small dish costs 2.9 and one large dish costs 3.9. This means that 2 small and 4 large dishes cost

$2.9\cdot 2 + 3.9 \cdot 4=21.4$