Connect Problem $01-13($algo$)$

Next Friday, you plan to sell cakes at a bake sale to raise money for your school. You plan to charge $$30$ per cake, and you anticipate that you will sell $10$ cakes. You can either purchase cakes to sell or bake them yourself. If you purchase the cakes, they will cost $$23$ each. If you bake your own cakes, your cost depends upon the number of cakes you bake, as shown in the table below.

$\backslash$table$[[\backslash$table$[[$Number of cakes$],[$you bake$]],\backslash$table$[[$Total cost of$],[$baked cakes$],[($$$)]]],[0,0],[1,10],[2,22],[3,36],[4,52],[5,70],[6,90],[7,112],[8,136],[9,162],[10,190]]$

a$.$ How many cakes should you bake? How many cakes should you purchase?

Instructions: Enter your answer as a whole number.

Bake cake$($s$)$ and purchase cake$($s$).$

b$.$ Given your answer to part a$,$ how much in total will the $10$ cakes cost you?

Instructions: Enter your answer as a whole number.

$

c$.$ How much would it have cost you to bake all $10$ cakes?