Question

Please help!!!

System of Equations Applications


Bill and Cody are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of double chocolate chip cookie dough. Bill sold 9 packages of white chocolate chip cookie dough and 2 packages of double chocolate cookie dough for a total of $200. Cody sold 2 packages of white chocolate chip cookie dough and 13 packages of double chocolate chip cookie dough for a total of $283. find the cost each of one package of white chocolate chip cookie dough and one package of double chocolate chip cookie dough.

Answer 1

Bill: 9w+2d=$200
Cody:. 2w+13d= $283

2(9w+2d=$200)
-9(2w+13d=$283)

18w+4d=$400
-18w-117d=-$2547

-113d= -2147

d= $19

9w+2(19)=200

9w+38=200

9w= 162

w= $18

double chocolate chip cookie dough:$19
white chocolate chip cookie dough: $18

Answer 2

We will use w for white choco cookies and b for choco cookies.
Bill sold 9 for w and 2 for b for a total of 200. So 9w + 2b = 200
Cody sold 2 for w and 13 for b for a total of 283. So 2w + 13b = 283

Lets solve by elimination.


`\begin{bmatrix}9w+2b=200\\ 2w+13b=283\end{bmatrix}`


`\mathrm{Multiply\:}9w+2b=200\mathrm{\:by\:}2:\quad 18w+4b=400`

`\mathrm{Multiply\:}2w+13b=283\mathrm{\:by\:}9:\quad 18w+117b=2547`


`\begin{bmatrix}18w+4b=400\\ 18w+117b=2547\end{bmatrix}`

18w + 117b = 2547
-
18w + 4b = 400
/
113b = 2147


`\begin{bmatrix}18w+4b=400\\ 113b=2147\end{bmatrix}`


`113b=2147 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}113 \ \textgreater \ (113b)/(113)=(2147)/(113) \ \textgreater \ b=19`


`\mathrm{For\:}18w+4b=400\mathrm{\:plug\:in\:}\ \:b=19`


`18w+4\cdot \:19=400 \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:4\cdot \:19=76`


`18w+76=400 \ \textgreater \ \mathrm{Subtract\:}76\mathrm{\:from\:both\:sides}`


`18w+76-76=400-76 \ \textgreater \ 18w=324 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}18`


`(18w)/(18)=(324)/(18) \ \textgreater \ w=18`

Therefore the cost of the white chocolate chip cookies is $18 and the double choco is $19