Thread: Let "x" represent, let "y" represent. write equation for costs and revenue

Hi everyone,

I have a multi part question that I am unsure how to solve. Here it is (sorry it's kind of long):

Lee is starting a cake decorating and baking business. She had to invest $462 in her business to get started. She pays $4 per cake for ingredients, and she sells each cake for $25.

a) Let x represent___________________________
Let y represent___________________________

b) write an equation that represents her costs.

c) write an equation that represents her revenue

d) does Lee make a profit or lose money for
15 cakes? 20 cakes? 25 cakes?

Thanks for any help. It is appreciated

a) i suggest you let x represent the number of cakes, and let y represent the profit (or loss) realized as a function of x.

b) what are these? for example, if Lee bakes one cake, that's $462 to get started, and $4 for the ingredients, which means Lee is $466 in the hole, unless she sells the cake.

c) in general: profit = revenue - costs. the profit made (or lost) will depend on the number of cakes. as i showed above, 1 cake has a cost of $466, if it sells, that is $25 revenue, defraying the loss to a mere $441 dollars in the hole.

d) if you do (b) & (c), you should be able to use what i said for (c) to get a formula for profit/loss.

Originally Posted by butcshe

Hi everyone,

I have a multi part question that I am unsure how to solve. Here it is (sorry it's kind of long):

Lee is starting a cake decorating and baking business. She had to invest $462 in her business to get started. She pays $4 per cake for ingredients, and she sells each cake for $25.

a) Let x represent___number of cakes she makes_
Let y represent___her total costs___________

b) write an equation that represents her costs. y = 462 + 4x

c) write an equation that represents her revenue R = 25x

d) does Lee make a profit or lose money for
15 cakes? 20 cakes? 25 cakes?

you can finish part (d) ...

Hey Deveno and Skeeter,

Thanks so much for your help. Things are much clearer now. Much appreciated.

what Lee needs to know (as any good businesswoman should) is: when is her profit 0? (this is "the break-even point"). how many cakes does this require she sell?