A café sells sandwiches and drinks at fixed prices. Receipt A : $2$ sandwiches and $3$ drinks co

Question

A café sells sandwiches and drinks at fixed prices.

Receipt A : $2$ sandwiches and $3$ drinks cost $\$16$.
Receipt B : $4$ sandwiches and $6$ drinks cost $\$35$.

Explain why the receipts cannot both be correct under the fixed-price assumption.
If Receipt A is correct, what should Receipt B’s total be?
After correcting Receipt B, can you determine the individual prices uniquely? Explain.
A third receipt shows that $1$ sandwich and $1$ drink cost $\$6$. Use this information with Receipt A to find both prices.

Accepted Answer

(a) Inconsistent; (b) $\$32$; (c) Not unique; (d) Sandwich $\$2$, Drink $\$4$.

Simultaneous Equations