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The ratio of the number of brownies sold to the number of cookies sold is 3: 5.

Each piece of brownie was sold for $1 more than each piece of cookie. Eric

collected $154 for all brownies and cookies sold. He collected $44 more from the 

sale of brownies than the sale of cookies. How many brownies were sold?

 Sep 7, 2021
 #1
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Let x = number of brownies sold.

      y = number of cookies sold.

 

 : x/y = 3/5

 =>   5x - 3y = 0 -------- 1

Let $p be the price of each piece of cookies.

 Given that, each piece of bro is sold for $1

 more than each piece of cookie.

 : The price of each piece of brownie is $(8+1)

Eric collected $154 for all brownies and cookies sold.

  : (8+1)x + Py = 154 -------- 2

Also, Eric collected $44 more from the sale of brownies than the sale of cookies.

  :     (p+1)x = 44 + py

Substituting (p+1) x = 44+py in equation 2 we, get

              44 + py + py = 154

              =>   2py = 110

              =>   py = 55 ------ 3

 From equation 1, y = 5/3x.

  : Substituting value y = 5/3x in equation 3, we get

              P(5/3x) = 55 => px = \({55 * 3 \over 5} = 33{}{}\)

             => px * 33 -----4

 Substituting values of px = 33 of py = 55 in

 equation 2, we have

     (P+1)x + Py = 154

    => Px + x + Py = 154 

    => 33 + x + 55 = 154   =>  x = 154 - 33 - 55

                                         => x = 66

  Substituting  x = 66 in equation 1, we have

     5x - 3y = 0   =>  5(66)- 3y = 0 =>  3y = 330

                                                     => y = 110

    Substituting  x = 66 in equation 4, we have

         px = 33  =>  p (66) = 33 =>  P=0.5

: Each piece of cookie is sold at $0.5 and each piece of brownie is sold at $1.5

The number of cookie sold = y = 110.

The number of brownies sold is x = 66.

:  66 pieces of brownies were sold.

 Sep 10, 2021

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