Makayla and John are selling cookie dough for a school fundraiser. Customers can buy chocolate chip or gingerbread cookie dough. Makayla sold 8 packages of chocolate chip and 12 packages of gingerbread cookie dough for a total of $364. John sold 1 package of chocolate chip and 4 packages of gingerbread cookie dough for a total of $93. Find the cost each of one package of chocolate chip cookie dough and one package of gingerbread cookie dough.

The cost per package is $---- for chocolate chip and $----- for gingerbread.

Lets give a letter value for the chocolate chip and gingerbread cookies. Lets let C= Chocolate chip and G= Gingerbread For Makayla we can set her equation as 8c+12g=364

For John we can leave it as c+4g=93

To solve the equation we would have to substitute the second one into the first one to solve for gingerbread. Lets isolate C to make C=(93-4g)

We can do this because we know that C=93-4g so we can replace the C variable in the first equation with C=93-4g

8(93-4g) + 12g = 364

744 - 32g + 12g = 364

-32g + 12g = 364 - 744

-20g = -380

g = -380/-20

So we know that g=19 dollars. So one gingerbread cookie dough is $19

So now we can plug in the answer of g which was 19 then solve for C

c = 93 - 4(19)

c = $17 for the chip dough

semsee45 semsee45 · Answer 2 · 2022-09-03T10:35:43+02:00

Answer:

The cost per package is $17 for chocolate chip and $19 for gingerbread.

Step-by-step explanation:

Define the variables:

Let x = cost of chocolate chip cookie dough (in dollars)
Let y = cost of gingerbread cookie dough (in dollars)

Given information:

Makayla sold 8 packages of chocolate chip and 12 packages of gingerbread cookie dough for a total of $364.
John sold 1 package of chocolate chip and 4 packages of gingerbread cookie dough for a total of $93.

Create two equations using the defined variables and the given information:

[tex]\textsf{Equation 1}: \quad 8x+12y=364[/tex]

[tex]\textsf{Equation 2}: \quad x+4y=93[/tex]

Multiply Equation 2 by 3:

[tex]\implies 3 \cdot x + 3 \cdot 4y=3 \cdot 93[/tex]

[tex]\implies 3x+12y=279[/tex]

Subtract from Equation 1 to eliminate the term in y:

[tex]\begin{array}{lrl}& 8x+12y =&364\\- & (3x+12y =&279)\\\cline{1-3} & 5x \phantom{+12y)} =& \:\:85\end{array}[/tex]

Solve for x:

[tex]\implies 5x=85[/tex]

[tex]\implies \dfrac{5x}{5}=\dfrac{85}{5}[/tex]

[tex]\implies x=17[/tex]

Substitute the found value of x into Equation 2 and solve for y:

[tex]\implies x+4y=93[/tex]

[tex]\implies 17+4y=93[/tex]

[tex]\implies 17+4y-17=93-17[/tex]

[tex]\implies 4y=76[/tex]

[tex]\implies \dfrac{4y}{4}=\dfrac{76}{4}[/tex]

[tex]\implies y=19[/tex]

Conclusion

Cost per package of chocolate chip cookie dough = $17.
Cost per package of gingerbread cookie dough = $19.

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