A baker will supply $22$ jumbo cinnamon rolls to a cafe at a price of $4.63$ dollars each. If she is offered $\$3.87$, then she will supply $4$ fewer rolls to the cafe. The cafe's demand for jumbo cinnamon rolls is given by $p = D(x) = -0.25x + 6.17$. What is the equilibrium point?
The answer was $13$ rolls sold at $\$2.92$ each
What would I do to find the answer to this? I tried $4.36 = -0.25 \cdot 22+b$ and $3.87 = -0.25 \cdot 19+b$ but it isn't working out so I'm not quite sure. Please comment any questions, thanks!
hint
You use the first condition (and the unspoken assumption that the supply function is linear) to write a linear supply function $S(x).$ You are given two points $(18,3.87)$ and $(22,4.63)$ so you can determine this line. Then just set $S(x)=D(x)$ and solve for $x.$