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Lamar, Sang and Ester are all baking desserts for the school bake sale. Lamar baked 12 more copkies than Sang, and Ester baked half as many cookies as Lamar. All together they baked 63 cookies. How many cookies did they each bake? Write an expression that represents how many cookies each person baked Use your expressions to write the equation that can be used to determine how many cookies each person baked. Label each part of your equation with the person that it represents.

Answer :

Let L be the number of cookies of Lamar, S the number of cookies of Sang and E the number of cookes of Ester.

Since Lamar baked 12 more cookes than Sang, we can write the following equation:

[tex]L=S+12[/tex]

Next, we have that Ester baked half as many cookies as Lamar, then we can write:

[tex]E=\frac{1}{2}L=\frac{1}{2}(S+12)[/tex]

finally, we have that they baked 63 cookes altogether, then we have:

[tex]L+S+E=63[/tex]

Using the values L = S + 12 and E = 1/2(S+12), we can find an equation and solve for S:

[tex]\begin{gathered} S+12+S+\frac{1}{2}(S+12)=63 \\ \Rightarrow2S+12+\frac{1}{2}S+6=63 \\ \Rightarrow\frac{5}{2}S+18=63 \\ \Rightarrow\frac{5}{2}S=63-18=45 \\ \Rightarrow S=45(\frac{2}{5})=\frac{90}{5}=18 \\ S=18 \end{gathered}[/tex]

We have that Sang baked 18 cookies, then we can use this value to find how many cookies baked Lamar and Ester:

[tex]\begin{gathered} L=12+18=30 \\ E=\frac{1}{2}(12+18)=\frac{1}{2}(30)=15 \end{gathered}[/tex]

therefore, Lamar baked 30 cookes, Sang baked 18 cookies and Ester baked 15 cookies

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