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Gabriella and Ming are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of gingerbread cookie dough. Gabriella sold 11 packages of white chocolate chip cookie dough and 2 packages of gingerbread cookie dough for a total of $225. Ming sold 8 packages of white chocolate chip cookie dough and 10 packages of gingerbread cookie dough for a total of $ 326. What is the cost each of one package of white chocolate chip cookie dough and one package of gingerbread cookie dough ?

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sqdancefan

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Answer:

  • white chocolate chip: $17
  • gingerbread: $19

Step-by-step explanation:

We can let x and y represent the costs of packages of white chocolate chip and gingerbread cookie dough, respectively. Then the two sales can be represented by ...

  11x +2y = 225

  8x +10y = 326

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There are several ways a system of equations like this can be solved. One of my favorites is to use a graphing calculator (see attached).

We can also use substitution. We see that the coefficients of y are simply related, so we can use ...

  2y = 225 -11x . . . . from equation 1

  8x +5(2y) = 326 . . . rearrange equation 2

  8x +5(225 -11x) = 326 . . . . substitute for 2y

  -47x +1125 = 326 . . . . simplify

  799 = 47x . . . . . . . add 47x-326

  17 = x . . . . . . . . . . . divide by 47

  2y = 225 -11(17) = 38

  y = 19 . . . . . . divide by 2

The package costs are ...

  white chocolate chip dough: $17

  gingerbread dough: $19.

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