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Math Help - Let "x" represent, let "y" represent. write equation for costs and revenue

  1. #1
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    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
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  2. #2
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    Re: Let "x" represent, let "y" represent. write equation for costs and revenue

    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.
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  3. #3
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    Re: Let "x" represent, let "y" represent. write equation for costs and revenue

    Quote Originally Posted by butcshe View Post
    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) ...
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  4. #4
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    Re: Let "x" represent, let "y" represent. write equation for costs and revenue

    Hey Deveno and Skeeter,

    Thanks so much for your help. Things are much clearer now. Much appreciated.
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  5. #5
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    Re: Let "x" represent, let "y" represent. write equation for costs and revenue

    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?
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